College Algebra
1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: OpenStax
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5.1, Problem 4SE
What is another name for the standard form of aquadratic
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Complete the table below. For solutions, round to the nearest whole
number.
Let the universal set be whole numbers 1
through 20 inclusive. That is,
U = {1, 2, 3, 4, . . ., 19, 20}. Let A, B, and C
be subsets of U.
Let A be the set of all prime numbers:
A = {2, 3, 5, 7, 11, 13, 17, 19}
Let B be the set of all odd numbers:
B = {1,3,5,7, . . ., 17, 19}
Let C be the set of all square numbers:
C = {1,4,9,16}
A research team consists of 4 senior researchers and 10 research assistants. The team needs to select 2 senior researchers and 2 research assistants to attend a conference. How many different ways can the group being sent to the conference be formed?
Chapter 5 Solutions
College Algebra
Ch. 5.1 - A coordinate grid has been superimposed over the...Ch. 5.1 - Given the equation g(x)=13+x26x, write the...Ch. 5.1 - Find the domain and range of f(x)=2(x47)2+811.Ch. 5.1 - In a separate Try It, we found the standard and...Ch. 5.1 - A rock is thrown upward from the top of a 112-foot...Ch. 5.1 - Explain the advantage of writing a...Ch. 5.1 - How can the vertex of a parabola be used in...Ch. 5.1 - Explain why the condition of a0 is imposed inthe...Ch. 5.1 - What is another name for the standard form of...Ch. 5.1 - What two algebraic methods can be used to find...
Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, rewrite the quadratic...Ch. 5.1 - For the following exercises, determine whether...Ch. 5.1 - For the following exercises, determine whether...Ch. 5.1 - For the following exercises, determine whether...Ch. 5.1 - For the following exercises, determine whether...Ch. 5.1 - For the following exercises, determine whether...Ch. 5.1 - For the following exercises, determine whether...Ch. 5.1 - For the following exercises, determine whether...Ch. 5.1 - For the following exercises, determine the domain...Ch. 5.1 - For the following exercises, determine the domain...Ch. 5.1 - For the following exercises, determine the domain...Ch. 5.1 - For the following exercises, determine the domain...Ch. 5.1 - For the following exercises, determine the domain...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises, use the vertex (h, k)...Ch. 5.1 - For the following exercises. sketch a graph of the...Ch. 5.1 - For the following exercises. sketch a graph of the...Ch. 5.1 - For the following exercises. sketch a graph of the...Ch. 5.1 - For the following exercises. sketch a graph of the...Ch. 5.1 - For the following exercises. sketch a graph of the...Ch. 5.1 - For the following exercises. sketch a graph of the...Ch. 5.1 - For the following exercises, write the equation...Ch. 5.1 - For the following exercises, write the equation...Ch. 5.1 - For the following exercises, write the equation...Ch. 5.1 - For the following exercises, write the equation...Ch. 5.1 - For the following exercises, write the equation...Ch. 5.1 - For the following exercises, write the equation...Ch. 5.1 - For the following exercises. use the table of...Ch. 5.1 - For the following exercises. use the table of...Ch. 5.1 - For the following exercises. use the table of...Ch. 5.1 - For the following exercises. use the table of...Ch. 5.1 - For the following exercises. use the table of...Ch. 5.1 - For the following exercises, use a calculator to...Ch. 5.1 - For the following exercises, use a calculator to...Ch. 5.1 - For the following exercises, use a calculator to...Ch. 5.1 - For the following exercises, use a calculator to...Ch. 5.1 - For the following exercises, use a calculator to...Ch. 5.1 - For the following exercises, use the vertex of the...Ch. 5.1 - For the following exercises, use the vertex of the...Ch. 5.1 - For the following exercises, use the vertex of the...Ch. 5.1 - For the following exercises, use the vertex of the...Ch. 5.1 - For the following exercises, write the equation of...Ch. 5.1 - For the following exercises, write the equation of...Ch. 5.1 - For the following exercises, write the equation of...Ch. 5.1 - For the following exercises, write the equation of...Ch. 5.1 - For the following exercises, write the equation of...Ch. 5.1 - For the following exercises, write the equation of...Ch. 5.1 - Find the dimensions of the rectangular...Ch. 5.1 - Find the dimensions of the rectangular corral...Ch. 5.1 - Find the dimensions of the rectangular...Ch. 5.1 - Among all of the pairs of numbers whose sum is...Ch. 5.1 - Among all of the pairs of numbers whose...Ch. 5.1 - Suppose that the price per unit in dollars ofa...Ch. 5.1 - A rocket is launched in the air. Its height, in...Ch. 5.1 - A ball is thrown in the air from the top of a...Ch. 5.1 - A soccer stadium holds 62,000 spectators. With...Ch. 5.1 - A farmer finds that if she plants 75 trees per...Ch. 5.2 - Which functions are power functions?...Ch. 5.2 - Describe in words and symbols the and behavior of...Ch. 5.2 - Identify the degree, leading term, and leading...Ch. 5.2 - Describe the end behavior, and determine a...Ch. 5.2 - Given the function f(x)=0.2(x2)(x+1)(x5), express...Ch. 5.2 - Given the polynomial function f(x)=2x36x220x,...Ch. 5.2 - Without graphing the function, determine the...Ch. 5.2 - What can we conclude about the polynomial...Ch. 5.2 - Given the function f(x)=0.2(x2)(x+1)(x5),...Ch. 5.2 - Explain the difference between the coefficientof a...Ch. 5.2 - If a polynomial function is in factored form,...Ch. 5.2 - In general, explain the end behavior of a...Ch. 5.2 - What is the relationship between the degree of...Ch. 5.2 - What can we conclude if, in general, the graph of...Ch. 5.2 - For the following exercises, identify the function...Ch. 5.2 - For the following exercises, identify the function...Ch. 5.2 - For the following exercises, identify the function...Ch. 5.2 - For the following exercises, identify the function...Ch. 5.2 - For the following exercises, identify the function...Ch. 5.2 - For the following exercises, identify the function...Ch. 5.2 - For the following exercises, find the degree and...Ch. 5.2 - For the following exercises, find the degree and...Ch. 5.2 - For the following exercises, find the degree and...Ch. 5.2 - For the following exercises, find the degree and...Ch. 5.2 - For the following exercises, find the degree and...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, determine the end...Ch. 5.2 - For the following exercises, find the intercepts...Ch. 5.2 - For the following exercises, find the intercepts...Ch. 5.2 - For the following exercises, find the intercepts...Ch. 5.2 - For the following exercises, find the intercepts...Ch. 5.2 - For the following exercises, find the intercepts...Ch. 5.2 - For the following exercises, find the intercepts...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine the least...Ch. 5.2 - For the following exercises, determine whether the...Ch. 5.2 - For the following exercises, determine whether the...Ch. 5.2 - For the following exercises, determine whether the...Ch. 5.2 - For the following exercises, determine whether the...Ch. 5.2 - For the following exercises, determine whether the...Ch. 5.2 - For the following exercises, determine whether the...Ch. 5.2 - For the following exercises, determine whether the...Ch. 5.2 - For the following exercises, make a table to...Ch. 5.2 - For the following exercises, make a table to...Ch. 5.2 - For the following exercises, make a table to...Ch. 5.2 - For the following exercises, make a table to...Ch. 5.2 - For the following exercises, make a table to...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, graph the polynomial...Ch. 5.2 - For the following exercises, use the information...Ch. 5.2 - For the following exercises, use the information...Ch. 5.2 - For the following exercises, use the information...Ch. 5.2 - For the following exercises, use the information...Ch. 5.2 - For the following exercises, use the information...Ch. 5.2 - For the following exercises, use the written...Ch. 5.2 - For the following exercises, use the written...Ch. 5.2 - For the following exercises, use the written...Ch. 5.2 - For the following exercises, use the written...Ch. 5.2 - For the following exercises, use the written...Ch. 5.3 - Find the y-and x-intercepts of the function...Ch. 5.3 - Use the graph of the function of degree 5 in...Ch. 5.3 - Sketch a graph of f(x)=14x(x1)4(x+3)3.Ch. 5.3 - Show that the function f(x)=7x59x4x2 has at least...Ch. 5.3 - Given the graph shown in Figure 20, write a...Ch. 5.3 - Use technology to find the maximum and minimum...Ch. 5.3 - What is the difference between an x-intercept anda...Ch. 5.3 - If a polynomial function of degree n has n...Ch. 5.3 - Explain how the Intermediate Value Theorem...Ch. 5.3 - Explain how the factored form of the...Ch. 5.3 - If the graph of a polynomial just touches the...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x- or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x-or...Ch. 5.3 - For the following exercises, find the x- or...Ch. 5.3 - For the following exercises, find the x- or...Ch. 5.3 - For the following exercises, use the Intermediate...Ch. 5.3 - For the following exercises, use the Intermediate...Ch. 5.3 - For the following exercises, use the Intermediate...Ch. 5.3 - For the following exercises, use the Intermediate...Ch. 5.3 - For the following exercises, use the Intermediate...Ch. 5.3 - For the following exercises, use the Intermediate...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, find the zeros and...Ch. 5.3 - For the following exercises, graph the polynomial...Ch. 5.3 - For the following exercises, graph the polynomial...Ch. 5.3 - For the following exercises, graph the polynomial...Ch. 5.3 - For the following exercises, graph the polynomial...Ch. 5.3 - For the following exercises, graph the polynomial...Ch. 5.3 - For the following exercises, graph the polynomial...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, use the graph to...Ch. 5.3 - For the following exercises, use the graph to...Ch. 5.3 - For the following exercises, use the graph to...Ch. 5.3 - For the following exercises, use the graph to...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use the given...Ch. 5.3 - For the following exercises, use a calculator to...Ch. 5.3 - For the following exercises, use a calculator to...Ch. 5.3 - For the following exercises, use a calculator to...Ch. 5.3 - For the following exercises, use a calculator to...Ch. 5.3 - For the following exercises, use a calculator to...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, use the graphs to...Ch. 5.3 - For the following exercises, write the polynomial...Ch. 5.3 - For the following exercises, write the polynomial...Ch. 5.3 - For the following exercises, write the polynomial...Ch. 5.3 - For the following exercises, write the polynomial...Ch. 5.3 - For the following exercises, write the polynomial...Ch. 5.4 - Divide 16x312x2+20x3 by 4x+5.Ch. 5.4 - Use synthetic division to divide 3x4+18x33x+40 by...Ch. 5.4 - The area ofa rectangle is given by 3x3+14x223x+6....Ch. 5.4 - If division of a polynomial by a binomial...Ch. 5.4 - If a polynomial of degree n is divided by a...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use long division to...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use the graph of the...Ch. 5.4 - For the following exercises, use the graph of the...Ch. 5.4 - For the following exercises, use the graph of the...Ch. 5.4 - For the following exercises, use the graph of the...Ch. 5.4 - For the following exercises, use the graph of the...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use a calculator with...Ch. 5.4 - For the following exercises, use a calculator with...Ch. 5.4 - For the following exercises, use a calculator with...Ch. 5.4 - For the following exercises, use a calculator with...Ch. 5.4 - For the following exercises, use a calculator with...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use synthetic...Ch. 5.4 - For the following exercises, use the given length...Ch. 5.4 - For the following exercises, use the given length...Ch. 5.4 - For the following exercises, use the given length...Ch. 5.4 - For the following exercises, use the given volume...Ch. 5.4 - For the following exercises, use the given volume...Ch. 5.4 - For the following exercises, use the given volume...Ch. 5.4 - For the following exercises, use the given volume...Ch. 5.4 - For the following exercises, use the given volume...Ch. 5.4 - For the following exercises, use the given volume...Ch. 5.4 - For the following exercises, use the given volume...Ch. 5.5 - Use the Remainder Theorem to evaluate...Ch. 5.5 - Use the Factor Theorem to find the zeros of...Ch. 5.5 - Use the Rational Zero Theorem to find the rational...Ch. 5.5 - Find the zeros of f(x)=2x3+5x211x+4.Ch. 5.5 - Find a third degree polynomial with real...Ch. 5.5 - Use Descartes’ Rule of Signs to determine the...Ch. 5.5 - A shipping container in the shape of a rectangular...Ch. 5.5 - Describe a use for the Remainder Theorem.Ch. 5.5 - Explain why the Rational Zero Theorem does...Ch. 5.5 - What is the difference between rational and...Ch. 5.5 - If Descartes’ Rule of Signs reveals a no changeof...Ch. 5.5 - If synthetic division reveals a zero, why should...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, construct a...Ch. 5.5 - For the following exercises, construct a...Ch. 5.5 - For the following exercises, construct a...Ch. 5.5 - For the following exercises, construct a...Ch. 5.5 - For the following exercises, construct a...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.5 - For the following exercises, find the dimensions...Ch. 5.6 - Use arrow notation to describe the end behavior...Ch. 5.6 - Sketch the graph, and find the horizontal and...Ch. 5.6 - There are 1,200 freshmen and 1,500 sophomores at a...Ch. 5.6 - Find the domain of f(x)=4x5(x1)(x5).Ch. 5.6 - Find the vertical asymptotes and removable...Ch. 5.6 - Find the vertical and horizontal asymptotes of the...Ch. 5.6 - Given the reciprocal squared function that is...Ch. 5.6 - Given the function f(x)=(x+2)2(x2)2(x1)2(x3), use...Ch. 5.6 - What is the fundamental difference in the...Ch. 5.6 - What is the fundamental difference in the graphsof...Ch. 5.6 - If the graph of a rational function has a...Ch. 5.6 - Can a graph of a rational function have no...Ch. 5.6 - Can a graph of a rational function have...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, identify the removal...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, express a rational...Ch. 5.6 - For the following exercises, express a rational...Ch. 5.6 - For the following exercises, use the given...Ch. 5.6 - For the following exercises, use the given...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.7 - Show that f(x)=x+53 and f1(x)=3x5 are inverses.Ch. 5.7 - Find the inverse function of f(x)=x+43Ch. 5.7 - Find the inverse of the function f(x)=x2+1, on the...Ch. 5.7 - Restrict the domain and then find the inverse of...Ch. 5.7 - Find the inverse of the function f(x)=x+3x2.Ch. 5.7 - Explain why we cannot find inverse functions for...Ch. 5.7 - Why must we restrict the domain of a...Ch. 5.7 - When finding the inverse of a radical function,...Ch. 5.7 - The inverse of a quadratic function will always...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.8 - The quantity y varies directly with the square of...Ch. 5.8 - A quantity y varies inversely with the square of...Ch. 5.8 - A quantity x varies directly with the square of y...Ch. 5.8 - What is true of the appearance of graphs...Ch. 5.8 - If two variables vary inversely what will an...Ch. 5.8 - Is there a limit to the number of variables...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5 - For the following exercises, write the quadratic...Ch. 5 - For the following exercises, write the quadratic...Ch. 5 - For the following problems, find the equation of...Ch. 5 - For the following problems, find the equation of...Ch. 5 - For the following exercises, complete the task. 5....Ch. 5 - For the following exercises, complete the task. An...Ch. 5 - For the following exercises, determine if the...Ch. 5 - For the following exercises, determine if the...Ch. 5 - For the following exercises, determine if the...Ch. 5 - For the following exercises, determine end...Ch. 5 - For the following exercises, determine end...Ch. 5 - For the following exercises, determine end...Ch. 5 - For the following exercises, find all zeros of the...Ch. 5 - For the following exercises, find all zeros of the...Ch. 5 - For the following exercises, find all zeros of the...Ch. 5 - For the following exercises, based on the given...Ch. 5 - For the following exercises, based on the given...Ch. 5 - For the following exercises. based on the given...Ch. 5 - For the following exercises, use long division to...Ch. 5 - For the following exercises, use long division to...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use Descartes’ Rule...Ch. 5 - For the following exercises, use Descartes’ Rule...Ch. 5 - For the following exercises. find the intercepts...Ch. 5 - For the following exercises. find the intercepts...Ch. 5 - For the following exercises, find the intercepts...Ch. 5 - For the following exercises. find the intercepts...Ch. 5 - For the following exercises, find the slant...Ch. 5 - For the following exercises, find the slant...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, solve the application...Ch. 5 - For the following exercises, solve the application...Ch. 5 - Give the degree and leading coefficient of the...Ch. 5 - Determine the and behavior of the polynomial...Ch. 5 - Determine the and behavior of the polynomial...Ch. 5 - Write the quadratic function in standard form....Ch. 5 - Given information about the graph of a quadratic...Ch. 5 - Solve the following application problem. A...Ch. 5 - Find all zeros of the following polynomial...Ch. 5 - Find all zeros of the following polynomial...Ch. 5 - Based on the graph, determine the zeros of the...Ch. 5 - Use long division to find the quotient. 2x3+3x4x+2Ch. 5 - Use synthetic division to find the quotient. If...Ch. 5 - Use synthetic division to find the quotient. If...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Given the following information about a polynomial...Ch. 5 - Given the following information about a polynomial...Ch. 5 - Use Descartes’ Rule of Signs to determine the...Ch. 5 - For the following rational functions, find the...Ch. 5 - For the following rational functions, find the...Ch. 5 - Find the slant asymptote of the rational function....Ch. 5 - Find the inverse of the function. f(x)=x2+4Ch. 5 - Find the inverse of the function. f(x)=3x34Ch. 5 - Find the inverse of the function. f(x)=2x+33x1Ch. 5 - Find the unknown value. y varies inversely as the...Ch. 5 - Find the unknown value. 27. y varies jointly with...Ch. 5 - Solve the following application problem. The...
Additional Math Textbook Solutions
Find more solutions based on key concepts
The numbers in the increasing order
Pre-Algebra Student Edition
Fill in each blank so that the resulting statement is true. An equation that expresses a relationship between t...
Algebra and Trigonometry (6th Edition)
76. Dew Point and Altitude The dew point decreases as altitude increases. If the dew point on the ground is 80°...
College Algebra with Modeling & Visualization (5th Edition)
Find the derivatives of the functions in Exercises 23–50.
43.
University Calculus: Early Transcendentals (4th Edition)
2. Source of Data In conducting a statistical study, why is it important to consider the source of the data?
Elementary Statistics
Fill in each blank so that the resulting statement is true. If n is a counting number, bn, read ______, indicat...
College Algebra (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- There are 25 different varieties of flowering plants found in a natural habitat you are studying. You are asked to randomly select 5 of these flowering plant varieties to bring back to your laboratory for further study. How many different combinations of are possible? That is, how many possible 5 plant subgroups can be formed out of the 25 total plants found?arrow_forwardA person is tossing a fair, two-sided coin three times and recording the results (either a Heads, H, or a Tails, T). Let E be the event that exactly two heads are tossed. Which of the following sets represent the event E? Group of answer choices {HHT, HTH, THH} {HHT, THH} {HHH, HHT, HTH, THH, TTT, TTH, THT, HTT} {HH}arrow_forwardTake Quiz 54m Exit Let the universal set be whole numbers 1 through 20 inclusive. That is, U = {1, 2, 3, 4, . . ., 19, 20}. Let A, B, and C be subsets of U. Let A be the set of all prime numbers: A = {2, 3, 5, 7, 11, 13, 17, 19} Let B be the set of all odd numbers: B = {1,3,5,7, • • , 17, 19} Let C be the set of all square numbers: C = {1,4,9,16} ☐ Question 2 3 pts Which of the following statement(s) is true? Select all that apply. (1) АСВ (2) A and C are disjoint (mutually exclusive) sets. (3) |B| = n(B) = 10 (4) All of the elements in AC are even numbers. ☐ Statement 1 is true. Statement 2 is true. Statement 3 is true. Statement 4 is true.arrow_forward
- ☐ Question 1 2 pts Let G be the set that represents all whole numbers between 5 and 12 exclusive. Which of the following is set G in standard set notation. (Roster Method)? O G = [5, 12] G = {5, 6, 7, 8, 9, 10, 11, 12} O G = (5, 12) OG = {6, 7, 8, 9, 10, 11}arrow_forwardSolve thisarrow_forwardint/PlayerHomework.aspx?homeworkId=689099898&questionId=1&flushed=false&cid=8120746¢erw BP Physical Geograph... HW Score: 0%, 0 of 13 points ○ Points: 0 of 1 Determine if the values of the variables listed are solutions of the system of equations. 2x - y = 4 3x+5y= - 6 x=1, y = 2; (1,-2) Is (1, 2) a solution of the system of equations? L No Yes iew an example Get more help - Aarrow_forward
- 12:01 PM Tue May 13 < AA ✓ Educatic S s3.amazona... A Assess Your... 目 accelerate-iu15-bssd.vschool.com S s3.amazona... Trigonometric Identities Module Exam Dashboard ... Dashboard ... Algebra 2 Pa... Algebra 2 Part 4 [Honors] (Acc. Ed.) (Zimmerman) 24-25 / Module 11: Trigonometric Identities i + 38% ✰ Start Page Alexis Forsythe All changes saved 10. A sound wave's amplitude can be modeled by the function y = −7 sin ((x-1) + 4). Within the interval 0 < x < 12, when does the function have an amplitude of 4? (Select all that apply.) 9.522 seconds 4.199 seconds 0.522 seconds 1.199 seconds Previous 10 of 20 Nextarrow_forwardJamal wants to save $48,000 for a down payment on a home. How much will he need to invest in an account with 11.8% APR, compounding daily, in order to reach his goal in 10 years? Round to the nearest dollar.arrow_forwardr nt Use the compound interest formula, A (t) = P(1 + 1)". An account is opened with an intial deposit of $7,500 and earns 3.8% interest compounded semi- annually. Round all answers to the nearest dollar. a. What will the account be worth in 10 years? $ b. What if the interest were compounding monthly? $ c. What if the interest were compounded daily (assume 365 days in a year)? $arrow_forward
- Kyoko has $10,000 that she wants to invest. Her bank has several accounts to choose from. Her goal is to have $15,000 by the time she finishes graduate school in 7 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal assuming they compound daily? (Hint: solve the compound interest formula for the intrerest rate. Also, assume there are 365 days in a year) %arrow_forward3:56 wust.instructure.com Page 0 Chapter 5 Test Form A of 2 - ZOOM + | Find any real numbers for which each expression is undefined. 2x 4 1. x Name: Date: 1. 3.x-5 2. 2. x²+x-12 4x-24 3. Evaluate when x=-3. 3. x Simplify each rational expression. x²-3x 4. 2x-6 5. x²+3x-18 x²-9 6. Write an equivalent rational expression with the given denominator. 2x-3 x²+2x+1(x+1)(x+2) Perform the indicated operation and simplify if possible. x²-16 x-3 7. 3x-9 x²+2x-8 x²+9x+20 5x+25 8. 4.x 2x² 9. x-5 x-5 3 5 10. 4x-3 8x-6 2 3 11. x-4 x+4 x 12. x-2x-8 x²-4 ← -> Copyright ©2020 Pearson Education, Inc. + 5 4. 5. 6. 7. 8. 9. 10. 11. 12. T-97arrow_forwardProblem #5 Suppose you flip a two sided fair coin ("heads" or "tails") 8 total times. a). How many ways result in 6 tails and 2 heads? b). How many ways result in 2 tails and 6 heads? c). Compare your answers to part (a) and (b) and explain in a few sentences why the comparison makes sense.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY