Precalculus: A Unit Circle Approach (3rd Edition)
3rd Edition
ISBN: 9780134433042
Author: J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2.6, Problem 28E
Determine upper and lower bounds on the zeros of the given function.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Chapter 2 Solutions
Precalculus: A Unit Circle Approach (3rd Edition)
Ch. 2.1 - 1. The graph of
is a ...Ch. 2.1 - Prob. 2ECh. 2.1 - The graph of
is symmetric with respect to the...Ch. 2.1 - The x-coordinate of the vertex of is given by ...Ch. 2.1 - True or False. The domain ofis.
Ch. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Match each quadratic function with its graph.
Ch. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Find the quadratic function that has the given...Ch. 2.1 - Find the quadratic function that has the given...Ch. 2.1 - Find the quadratic function that has the given...Ch. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Find the quadratic function that has the given...Ch. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Graph the given function by writing it in the...Ch. 2.1 - Graph the given function by writing it in the...Ch. 2.1 - Graph the given function by writing it in the...Ch. 2.1 - Graph the given function by writing it in the...Ch. 2.1 - Graph the given function by writing it in the...Ch. 2.1 - Graph the given function by writing it in the...Ch. 2.1 - Prob. 51ECh. 2.1 - Prob. 52ECh. 2.1 - Prob. 53ECh. 2.1 - (a) determine whether the graph of the given...Ch. 2.1 - Prob. 55ECh. 2.1 - Prob. 56ECh. 2.1 - Prob. 57ECh. 2.1 - (a) determine whether the graph of the given...Ch. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - Prob. 64ECh. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - Prob. 69ECh. 2.1 - Prob. 70ECh. 2.1 - Prob. 71ECh. 2.1 - Prob. 72ECh. 2.1 - Prob. 73ECh. 2.1 - Prob. 74ECh. 2.1 - Prob. 75ECh. 2.1 - Prob. 76ECh. 2.1 - Prob. 77ECh. 2.1 - Prob. 78ECh. 2.1 - Prob. 79ECh. 2.1 - Prob. 80ECh. 2.1 - Prob. 81ECh. 2.1 - Prob. 82ECh. 2.1 - Prob. 83ECh. 2.1 - Prob. 84ECh. 2.1 - Maximizing revenue. A revenue function is given by...Ch. 2.1 - Maximizing revenue. A demand function is given by,...Ch. 2.1 - Prob. 87ECh. 2.1 - Maximizing profit. A manufacturer produces x items...Ch. 2.1 - Prob. 89ECh. 2.1 - Prob. 90ECh. 2.1 - Enclosing playing fields. You have 600 meters of...Ch. 2.1 - Enclosing area on a budget. You budget $2400 for...Ch. 2.1 - Maximizing apple yield. From past surveys and...Ch. 2.1 - Prob. 94ECh. 2.1 - Prob. 95ECh. 2.1 - Prob. 96ECh. 2.1 - Prob. 97ECh. 2.1 - Prob. 98ECh. 2.1 - Motion of a projectile. A projectile is fired...Ch. 2.1 - Motion of a projectile. A projectile is shot...Ch. 2.1 - Architecture. A window is to be constructed in the...Ch. 2.1 - Prob. 102ECh. 2.1 - Prob. 103ECh. 2.1 - Prob. 104ECh. 2.1 - Prob. 105ECh. 2.1 - Foreclosed properties The graph shows the number...Ch. 2.1 - Find a quadratic function of the form that...Ch. 2.1 - Find a quadratic function of the form that...Ch. 2.1 - Prob. 109ECh. 2.1 - Prob. 110ECh. 2.1 - Prob. 111ECh. 2.1 - Find a quadratic function of the form that...Ch. 2.1 - Prob. 113ECh. 2.1 - Find two quadratic functions, one opening up and...Ch. 2.1 - Find two quadratic functions, one opening up and...Ch. 2.1 - Prob. 116ECh. 2.1 - Prob. 117ECh. 2.1 - Prob. 118ECh. 2.1 - Prob. 119ECh. 2.1 - Prob. 120ECh. 2.1 - Prob. 121ECh. 2.1 - Prob. 122ECh. 2.1 - Show that, for any two positive numbers x and a, ...Ch. 2.1 - Show that, for any two positive numbers x and a, ...Ch. 2.1 - Simplify each expression. Write your answers...Ch. 2.1 - Prob. 126ECh. 2.1 - Prob. 127ECh. 2.1 - Prob. 128ECh. 2.1 - Prob. 129ECh. 2.1 - Prob. 130ECh. 2.1 - Prob. 131ECh. 2.1 - Factor each expression.
Ch. 2.1 - Factor each expression.
Ch. 2.1 - Prob. 134ECh. 2.1 - Prob. 135ECh. 2.1 - Prob. 136ECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - If c is a zero of odd multiplicity for a...Ch. 2.2 - True or False. A curve that has a sharp corner can...Ch. 2.2 - True or False. The end behavior of any polynomial...Ch. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - For each polynomial function, find the degree, the...Ch. 2.2 - For each polynomial function, find the degree, the...Ch. 2.2 - Explain why the given function is not a polynomial...Ch. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Explain why the given function is not a polynomial...Ch. 2.2 - Explain why the given function is not a polynomial...Ch. 2.2 - Explain why the given function is not a polynomial...Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Match the polynomial function with its graph. Use...Ch. 2.2 - Match the polynomial function with its graph. Use...Ch. 2.2 - Match the polynomial function with its graph. Use...Ch. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Describe the end behavior of the polynomial...Ch. 2.2 - Describe the end behavior of the polynomial...Ch. 2.2 - Describe the end behavior of the polynomial...Ch. 2.2 - Prob. 40ECh. 2.2 - Describe the end behavior of the polynomial...Ch. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Find the real zeros of f and state the...Ch. 2.2 - Find the real zeros of f and state the...Ch. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Find the real zeros of f and state the...Ch. 2.2 - Prob. 51ECh. 2.2 - Use the Intermediate Value Theorem to show that...Ch. 2.2 - Use the Intermediate Value Theorem to show that...Ch. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.2 - Prob. 59ECh. 2.2 - Prob. 60ECh. 2.2 - Find the polynomial with a leading coefficient of...Ch. 2.2 - Find the polynomial with a leading coefficient of...Ch. 2.2 - Prob. 63ECh. 2.2 - Prob. 64ECh. 2.2 - Prob. 65ECh. 2.2 - Prob. 66ECh. 2.2 - Prob. 67ECh. 2.2 - Prob. 68ECh. 2.2 - Prob. 69ECh. 2.2 - Prob. 70ECh. 2.2 - Prob. 71ECh. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.2 - Prob. 74ECh. 2.2 - Prob. 75ECh. 2.2 - Prob. 76ECh. 2.2 - Drug reaction. Let
a. Find the zeros of f and...Ch. 2.2 - Prob. 78ECh. 2.2 - Prob. 79ECh. 2.2 - Prob. 80ECh. 2.2 - Prob. 81ECh. 2.2 - Prob. 82ECh. 2.2 - Prob. 83ECh. 2.2 - Prob. 84ECh. 2.2 - Making a box. From a rectangular piece of...Ch. 2.2 - Prob. 86ECh. 2.2 - Prob. 87ECh. 2.2 - Prob. 88ECh. 2.2 - Prob. 89ECh. 2.2 - Prob. 90ECh. 2.2 - Luggage dimensions. American Airlines requires...Ch. 2.2 - Prob. 92ECh. 2.2 - Prob. 93ECh. 2.2 - Prob. 94ECh. 2.2 - Prob. 95ECh. 2.2 - Prob. 96ECh. 2.2 - Prob. 97ECh. 2.2 - Prob. 98ECh. 2.2 - Prob. 99ECh. 2.2 - Prob. 100ECh. 2.2 - Prob. 101ECh. 2.2 - Prob. 102ECh. 2.2 - Prob. 103ECh. 2.2 - Prob. 104ECh. 2.2 - Prob. 105ECh. 2.2 - Prob. 106ECh. 2.2 - Prob. 107ECh. 2.2 - Prob. 108ECh. 2.2 - Prob. 109ECh. 2.2 - Prob. 110ECh. 2.2 - Prob. 111ECh. 2.2 - Prob. 112ECh. 2.2 - Prob. 113ECh. 2.2 - Prob. 114ECh. 2.2 - Prob. 115ECh. 2.2 - Prob. 116ECh. 2.2 - Prob. 117ECh. 2.2 - Prob. 118ECh. 2.2 - Prob. 119ECh. 2.2 - Prob. 120ECh. 2.2 - Prob. 121ECh. 2.2 - Prob. 122ECh. 2.2 - Prob. 123ECh. 2.2 - Prob. 124ECh. 2.2 - Prob. 125ECh. 2.2 - Prob. 126ECh. 2.2 - Prob. 127ECh. 2.2 - Prob. 128ECh. 2.2 - Prob. 129ECh. 2.2 - Prob. 130ECh. 2.2 - Prob. 131ECh. 2.2 - Prob. 132ECh. 2.2 - Prob. 133ECh. 2.2 - Prob. 134ECh. 2.2 - Prob. 135ECh. 2.2 - Prob. 136ECh. 2.2 - Prob. 137ECh. 2.2 - Prob. 138ECh. 2.3 - Consider the equation x23x+5=x2+1x4x+5 . If both...Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Use long division to find the quotient and the...Ch. 2.3 - Use long division to find the quotient and the...Ch. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Use synthetic division to find the quotient and...Ch. 2.3 - Use synthetic division to find the quotient and...Ch. 2.3 - Use synthetic division to find the quotient and...Ch. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Use synthetic division to find the quotient and...Ch. 2.3 - Use synthetic division to find the quotient and...Ch. 2.3 - Use synthetic division and the Remainder Theorem...Ch. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Use the Factor Theorem to show that the first...Ch. 2.3 - Use the Factor Theorem to show that the first...Ch. 2.3 - Use the Factor Theorem to show that the first...Ch. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Find the value of k for which the first polynomial...Ch. 2.3 - Find the value of k for which the first polynomial...Ch. 2.3 - Use the Factor Theorem to show that the first...Ch. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Find the set of possible rational zeros of the...Ch. 2.3 - Find the set of possible rational zeros of the...Ch. 2.3 - Find all rational zeros of the given polynomial...Ch. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Find all rational zeros of the given polynomial...Ch. 2.3 - Find all rational zeros of the given polynomial...Ch. 2.3 - Find all rational zeros of the given polynomial...Ch. 2.3 - Prob. 59ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.3 - Prob. 65ECh. 2.3 - Find all rational zeros of the given polynomial...Ch. 2.3 - First find all rational zeros of f, then use the...Ch. 2.3 - Prob. 68ECh. 2.3 - Prob. 69ECh. 2.3 - Prob. 70ECh. 2.3 - Prob. 71ECh. 2.3 - Prob. 72ECh. 2.3 - Prob. 73ECh. 2.3 - Prob. 74ECh. 2.3 - Use the Rational Zeros Test and synthetic division...Ch. 2.3 - Use the Rational Zeros Test and synthetic division...Ch. 2.3 - Prob. 77ECh. 2.3 - Prob. 78ECh. 2.3 - Prob. 79ECh. 2.3 - Prob. 80ECh. 2.3 - Prob. 81ECh. 2.3 - Prob. 82ECh. 2.3 - Prob. 83ECh. 2.3 - Sketch the graph of each polynomial function.
Ch. 2.3 - Sketch the graph of each polynomial function.
Ch. 2.3 - Prob. 86ECh. 2.3 - Prob. 87ECh. 2.3 - Prob. 88ECh. 2.3 - Prob. 89ECh. 2.3 - Prob. 90ECh. 2.3 - Prob. 91ECh. 2.3 - Prob. 92ECh. 2.3 - Total energy consumption. The total energy...Ch. 2.3 - Lottery sales. In the lottery game called Florida...Ch. 2.3 - Marine Corps. The total number of U.S. Marine...Ch. 2.3 - Prob. 96ECh. 2.3 - Prob. 97ECh. 2.3 - Prob. 98ECh. 2.3 - Prob. 99ECh. 2.3 - Prob. 100ECh. 2.3 - Shipping boxes. When two shipping boxes in the...Ch. 2.3 - Building a Pool. A builder is commissioned to...Ch. 2.3 - Making a box. A square piece of tin 18 inches on...Ch. 2.3 - Prob. 104ECh. 2.3 - Prob. 105ECh. 2.3 - Prob. 106ECh. 2.3 - Prob. 107ECh. 2.3 - Show that by considering the polynomial and...Ch. 2.3 - Show that there is no real number a such that is...Ch. 2.3 - Show that divides by considering the polynomial ...Ch. 2.3 - When the polynomial is divided by , the remainder...Ch. 2.3 - Prob. 112ECh. 2.3 - Prob. 113ECh. 2.3 - Prob. 114ECh. 2.3 - Prob. 115ECh. 2.3 - Prob. 116ECh. 2.3 - Show that the given number is irrational. [Hint:...Ch. 2.3 - Show that the given number is irrational. [Hint:...Ch. 2.3 - Show that the given number is irrational. [Hint:...Ch. 2.3 - Prob. 120ECh. 2.3 - Prob. 121ECh. 2.3 - Prob. 122ECh. 2.3 - Prob. 123ECh. 2.3 - Prob. 124ECh. 2.3 - Graph the line given by the equation.
Ch. 2.3 - Graph the line given by the equation.
Ch. 2.3 - Prob. 127ECh. 2.3 - Prob. 128ECh. 2.3 - Prob. 129ECh. 2.3 - Prob. 130ECh. 2.4 - A function f is rational if it can be expressed as...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - True or False. If the point a is not in the domain...Ch. 2.4 - Prob. 6ECh. 2.4 - True or False. The graph of a rational function...Ch. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Use the graph of the rational function f(x) to...Ch. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.4 - Prob. 59ECh. 2.4 - Prob. 60ECh. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Prob. 63ECh. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Use the six-step procedure on pages 196 to graph...Ch. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.4 - Prob. 71ECh. 2.4 - Prob. 72ECh. 2.4 - Prob. 73ECh. 2.4 - Prob. 74ECh. 2.4 - Prob. 75ECh. 2.4 - Prob. 76ECh. 2.4 - Prob. 77ECh. 2.4 - Prob. 78ECh. 2.4 - Use the six-step procedure on pages 196 to graph...Ch. 2.4 - Use the six-step procedure on pages 196 to graph...Ch. 2.4 - Find an equation of a rational function having the...Ch. 2.4 - Find an equation of a rational function having the...Ch. 2.4 - Prob. 83ECh. 2.4 - Prob. 84ECh. 2.4 - Prob. 85ECh. 2.4 - Prob. 86ECh. 2.4 - Prob. 87ECh. 2.4 - Find the oblique asymptote and sketch the graph of...Ch. 2.4 - Find the oblique asymptote and sketch the graph of...Ch. 2.4 - Prob. 90ECh. 2.4 - Prob. 91ECh. 2.4 - Prob. 92ECh. 2.4 - Prob. 93ECh. 2.4 - Use the following definition: Given a cost...Ch. 2.4 - Prob. 95ECh. 2.4 - Prob. 96ECh. 2.4 - Environment. Suppose an environmental agency...Ch. 2.4 - Biology. The growth function g(x) describes the...Ch. 2.4 - Prob. 99ECh. 2.4 - Prob. 100ECh. 2.4 - Book publishing. The printing and binding cost for...Ch. 2.4 - Prob. 102ECh. 2.4 - Prob. 103ECh. 2.4 - Prob. 104ECh. 2.4 - Use transformations of the graph of or to graph...Ch. 2.4 - Use transformations of the graph of or to graph...Ch. 2.4 - Use transformations of the graph of or to graph...Ch. 2.4 - Prob. 108ECh. 2.4 - Prob. 109ECh. 2.4 - Prob. 110ECh. 2.4 - Prob. 111ECh. 2.4 - Prob. 112ECh. 2.4 - Prob. 113ECh. 2.4 - Use Exercise 113 to sketch the graphs of and on...Ch. 2.4 - Recall that the inverse of a function is written...Ch. 2.4 - Let .Find and. Graph all three functions on the...Ch. 2.4 - Prob. 117ECh. 2.4 - Sketch the graph of . Discuss the end behavior of...Ch. 2.4 - The graph of the rational function crosses the...Ch. 2.4 - The graph of the rational function crosses the...Ch. 2.4 - Prob. 121ECh. 2.4 - Prob. 122ECh. 2.4 - Find an equation of a rational function f...Ch. 2.4 - Prob. 124ECh. 2.4 - Make up a rational function that has all of the...Ch. 2.4 - Make up a rational function that has all of the...Ch. 2.4 - Make up a rational function that has all of the...Ch. 2.4 - Prob. 128ECh. 2.4 - Prob. 129ECh. 2.4 - Prob. 130ECh. 2.4 - Prob. 131ECh. 2.4 - Ostwald's dilution law for electrolytes,
is used...Ch. 2.4 - Give an example of a rational function that...Ch. 2.4 - Give an example of a rational function that...Ch. 2.4 - Prob. 135ECh. 2.4 - Prob. 136ECh. 2.4 - Simplify each expression.
Ch. 2.4 - Prob. 138ECh. 2.4 - Simplify each expression.
Ch. 2.4 - Simplify each expression.
Ch. 2.4 - Solve each quadratic inequality.
Ch. 2.4 - Prob. 142ECh. 2.4 - Prob. 143ECh. 2.4 - Prob. 144ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - To solve a rational inequality, we begin by...Ch. 2.5 - For the rational inequalities or , the zeros of...Ch. 2.5 - True or False. A polynomial function P(x) may...Ch. 2.5 - Prob. 6ECh. 2.5 - True or False. A rational function R(x) always has...Ch. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Use the graph of the polynomial to solve the...Ch. 2.5 - Use the graph of the polynomial to solve the...Ch. 2.5 - Use the graph of the polynomial to solve the...Ch. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Prob. 32ECh. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Solve each polynomial inequality.
Ch. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Prob. 55ECh. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Prob. 69ECh. 2.5 - Prob. 70ECh. 2.5 - Prob. 71ECh. 2.5 - Prob. 72ECh. 2.5 - Prob. 73ECh. 2.5 - Prob. 74ECh. 2.5 - Prob. 75ECh. 2.5 - Prob. 76ECh. 2.5 - Prob. 77ECh. 2.5 - Prob. 78ECh. 2.5 - Prob. 79ECh. 2.5 - Prob. 80ECh. 2.5 - Prob. 81ECh. 2.5 - Prob. 82ECh. 2.5 - Prob. 83ECh. 2.5 - Prob. 84ECh. 2.5 - Prob. 85ECh. 2.5 - Prob. 86ECh. 2.5 - Prob. 87ECh. 2.5 - Prob. 88ECh. 2.5 - Prob. 89ECh. 2.5 - Prob. 90ECh. 2.5 - Prob. 91ECh. 2.5 - Prob. 92ECh. 2.5 - Prob. 93ECh. 2.5 - Prob. 94ECh. 2.5 - Prob. 95ECh. 2.5 - Prob. 96ECh. 2.5 - Prob. 97ECh. 2.5 - Prob. 98ECh. 2.5 - Prob. 99ECh. 2.5 - Prob. 100ECh. 2.5 - Prob. 101ECh. 2.5 - Prob. 102ECh. 2.5 - Prob. 103ECh. 2.5 - Prob. 104ECh. 2.5 - Prob. 105ECh. 2.5 - Prob. 106ECh. 2.5 - Prob. 107ECh. 2.5 - Prob. 108ECh. 2.5 - Prob. 109ECh. 2.5 - Prob. 110ECh. 2.5 - Prob. 111ECh. 2.5 - Prob. 112ECh. 2.5 - Prob. 113ECh. 2.5 - Prob. 114ECh. 2.5 - Prob. 115ECh. 2.5 - Prob. 116ECh. 2.5 - Prob. 117ECh. 2.5 - Prob. 118ECh. 2.5 - Prob. 119ECh. 2.5 - Prob. 120ECh. 2.5 - Prob. 121ECh. 2.5 - Prob. 122ECh. 2.5 - Prob. 123ECh. 2.5 - Prob. 124ECh. 2.5 - Prob. 125ECh. 2.5 - Prob. 126ECh. 2.5 - Prob. 127ECh. 2.5 - Prob. 128ECh. 2.5 - Prob. 129ECh. 2.5 - Prob. 130ECh. 2.5 - Prob. 131ECh. 2.5 - Prob. 132ECh. 2.5 - Prob. 133ECh. 2.5 - Prob. 134ECh. 2.5 - Use long division to verify that the polynomial Dx...Ch. 2.5 - Prob. 136ECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - The Fundamental Theorem of Algebra States that a...Ch. 2.6 - If P is a polynomial function with real...Ch. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Determine the possible number of positive and...Ch. 2.6 - Determine the possible number of positive and...Ch. 2.6 - Determine the possible number of positive and...Ch. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Determine the possible number of positive and...Ch. 2.6 - Determine the possible number of positive and...Ch. 2.6 - Determine the possible number of positive and...Ch. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Determine upper and lower bounds on the zeros of...Ch. 2.6 - Determine upper and lower bounds on the zeros of...Ch. 2.6 - Determine upper and lower bounds on the zeros of...Ch. 2.6 - Determine upper and lower bounds on the zeros of...Ch. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Find all solutions of the equation in the complex...Ch. 2.6 - Find all solutions of the equation in the complex...Ch. 2.6 - Find all solutions of the equation in the complex...Ch. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Find the remaining zeros of a polynomial with...Ch. 2.6 - Find the remaining zeros of a polynomial with...Ch. 2.6 - Prob. 45ECh. 2.6 - Prob. 46ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.6 - Prob. 49ECh. 2.6 - Prob. 50ECh. 2.6 - Prob. 51ECh. 2.6 - Use the given zero to find all the zeros for each...Ch. 2.6 - Use the given zero to find all the zeros for each...Ch. 2.6 - Use the given zero to find all the zeros for each...Ch. 2.6 - Prob. 55ECh. 2.6 - Prob. 56ECh. 2.6 - Prob. 57ECh. 2.6 - Prob. 58ECh. 2.6 - Prob. 59ECh. 2.6 - Find all zeros of each polynomial function.
Ch. 2.6 - Find all zeros of each polynomial function.
Ch. 2.6 - Find all zeros of each polynomial function.
Ch. 2.6 - Prob. 63ECh. 2.6 - Prob. 64ECh. 2.6 - Prob. 65ECh. 2.6 - Find an equation of a polynomial function of least...Ch. 2.6 - Find an equation of a polynomial function of least...Ch. 2.6 - Find an equation of a polynomial function of least...Ch. 2.6 - The solutions and 1 of the equation are called...Ch. 2.6 - The solutions of the equation , where n is a...Ch. 2.6 - Show that the polynomial function has six nonreal...Ch. 2.6 - Prob. 72ECh. 2.6 - Prob. 73ECh. 2.6 - Prob. 74ECh. 2.6 - Prob. 75ECh. 2.6 - Prob. 76ECh. 2.6 - Find an equation with real coefficients of a...Ch. 2.6 - Find an equation with real coefficients of a...Ch. 2.6 - Use the given zero and synthetic division to...Ch. 2.6 - Prob. 80ECh. 2.6 - Prob. 81ECh. 2.6 - Prob. 82ECh. 2.6 - Prob. 83ECh. 2.6 - Prob. 84ECh. 2.6 - Prob. 85ECh. 2.6 - Use Cardano's method to solve the equation .
Ch. 2.6 - a. Find the equation of the line in...Ch. 2.6 - a. Find the equation of the line in...Ch. 2.6 - Prob. 89ECh. 2.6 - Prob. 90ECh. 2.7 - Prob. 1ECh. 2.7 - Prob. 2ECh. 2.7 - y varies directly as the nth power of x if ...Ch. 2.7 - z varies jointly as x and y if .
Ch. 2.7 - True or False. In the equation , P varies directly...Ch. 2.7 - 6. True or False. In the equation , A varies...Ch. 2.7 - Prob. 7ECh. 2.7 - Prob. 8ECh. 2.7 - Prob. 9ECh. 2.7 - Prob. 10ECh. 2.7 - Use the four-step procedure to solve for the...Ch. 2.7 - Use the four-step procedure to solve for the...Ch. 2.7 - Prob. 13ECh. 2.7 - Prob. 14ECh. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Use the four-step procedure to solve for the...Ch. 2.7 - Use the four-step procedure to solve for the...Ch. 2.7 - Use the four-step procedure to solve for the...Ch. 2.7 - Prob. 23ECh. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Solve for the variable requested without...Ch. 2.7 - Solve for the variable requested without...Ch. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Converting units of length. Use the fact that ...Ch. 2.7 - Prob. 32ECh. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 37ECh. 2.7 - Prob. 38ECh. 2.7 - Prob. 39ECh. 2.7 - Prob. 40ECh. 2.7 - Prob. 41ECh. 2.7 - Prob. 42ECh. 2.7 - Illumination. The intensity I of illumination from...Ch. 2.7 - Prob. 44ECh. 2.7 - Prob. 45ECh. 2.7 - Prob. 46ECh. 2.7 - Horsepower. The horsepower H of an automobile...Ch. 2.7 - Prob. 48ECh. 2.7 - Prob. 49ECh. 2.7 - Prob. 50ECh. 2.7 - Prob. 51ECh. 2.7 - Prob. 52ECh. 2.7 - Prob. 53ECh. 2.7 - Prob. 54ECh. 2.7 - Prob. 55ECh. 2.7 - Prob. 56ECh. 2.7 - Prob. 57ECh. 2.7 - Bus service. The profit earned in running a bus...Ch. 2.7 - Weight of a sphere. The weight of a sphere is...Ch. 2.7 - Prob. 60ECh. 2.7 - Prob. 61ECh. 2.7 - Prob. 62ECh. 2.7 - Prob. 63ECh. 2.7 - Prob. 64ECh. 2.7 - Prob. 65ECh. 2.7 - Prob. 66ECh. 2.7 - Prob. 67ECh. 2.7 - Prob. 68ECh. 2 - Graph each quadratic function by finding (i)...Ch. 2 - Graph each quadratic function by finding (i)...Ch. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Determine whether the given quadratic function has...Ch. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Use Descartes's Rule of Signs and the Rational...Ch. 2 - Use Descartes's Rule of Signs and the Rational...Ch. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Find all of the zeros of real and nonreal, that...Ch. 2 - Find all of the zeros of real and nonreal, that...Ch. 2 - Find all of the zeros of real and nonreal, that...Ch. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Solve each equation in the complex number...Ch. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Solve each equation in the complex number...Ch. 2 - Show that the given equation has no rational...Ch. 2 - Show that the given equation has no rational...Ch. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Graph each rational function by following the...Ch. 2 - Graph each rational function by following the...Ch. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Solve each inequality.
Ch. 2 - Solve each inequality.
Ch. 2 - Solve each inequality.
Ch. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Variation. If s varies directly as the square of t...Ch. 2 - Variation. If y varies inversely as and if when...Ch. 2 - Missile path. A missile fired from the origin of a...Ch. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 86RECh. 2 - Prob. 87RECh. 2 - Maximizing area. A sheet of paper is 100 square...Ch. 2 - Maximizing profit. A manufacturer makes and sells...Ch. 2 - Meteorology. The function relates the atmospheric...Ch. 2 - Prob. 91RECh. 2 - Prob. 92RECh. 2 - Prob. 93RECh. 2 - Prob. 94RECh. 2 - Prob. 95RECh. 2 - Safe load. The safe load that a circular column...Ch. 2 - Spread of disease. An infectious cold virus...Ch. 2 - Prob. 98RECh. 2 - Prob. 1PTACh. 2 - Graph .
Ch. 2 - Prob. 3PTACh. 2 - Prob. 4PTACh. 2 - Prob. 5PTACh. 2 - Graph the polynomial function.
Ch. 2 - Find all of zeros of , given that 2 is one of the...Ch. 2 - Find the quotient of .
Ch. 2 - Use the Remainder Theorem to find the value of the...Ch. 2 - Prob. 10PTACh. 2 - Prob. 11PTACh. 2 - Prob. 12PTACh. 2 - Describe the end behaviour of .
Ch. 2 - Find the zeros and the multiplicity of each zero...Ch. 2 - Determine how many positive and how many negative...Ch. 2 - Prob. 16PTACh. 2 - Prob. 17PTACh. 2 - Prob. 18PTACh. 2 - Prob. 19PTACh. 2 - From a rectangular piece of cardboard, four...Ch. 2 - Find the x-intercepts of the graph of .
a.
b.
c....Ch. 2 - Which is the graph of ?
Ch. 2 - Prob. 3PTBCh. 2 - Prob. 4PTBCh. 2 - Prob. 5PTBCh. 2 - Prob. 6PTBCh. 2 - Prob. 7PTBCh. 2 - Find the quotient .
a.
b.
c.
d.
Ch. 2 - Use the Remainder Theorem to find the value of...Ch. 2 - Prob. 10PTBCh. 2 - Prob. 11PTBCh. 2 - For, list all possible rational zeros found by the...Ch. 2 - Prob. 13PTBCh. 2 - Prob. 14PTBCh. 2 - Determine how many positive and how many negative...Ch. 2 - The horizontal and the vertical asymptotes of the...Ch. 2 - Solve the inequality.
a.
b.
c.
d.
Ch. 2 - Prob. 18PTBCh. 2 - Prob. 19PTBCh. 2 - Prob. 20PTBCh. 2 - Find the distance between the points and.
Ch. 2 - Find the midpoint of the line segment joining ...Ch. 2 - Find the x- and y-intercepts of the graph of the...Ch. 2 - Prob. 4CRECh. 2 - Prob. 5CRECh. 2 - Prob. 6CRECh. 2 - Prob. 7CRECh. 2 - Find the slope–intercept form of the line...Ch. 2 - Prob. 9CRECh. 2 - Prob. 10CRECh. 2 - Prob. 11CRECh. 2 - Prob. 12CRECh. 2 - Prob. 13CRECh. 2 - Prob. 14CRECh. 2 - Let . Find.
Ch. 2 - Use transformations on to sketch the graph of each...Ch. 2 - Prob. 17CRECh. 2 - Prob. 18CRECh. 2 - Prob. 19CRECh. 2 - Prob. 20CRECh. 2 - Prob. 21CRECh. 2 - Prob. 22CRECh. 2 - Prob. 23CRECh. 2 - A drug manufactured by a pharmaceutical company is...Ch. 2 - The profit (in dollars) for a product is given by...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Use a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.) y = 100e0.01x (x, y) = y = 11,250 ×arrow_forward5. For the function y-x³-3x²-1, use derivatives to: (a) determine the intervals of increase and decrease. (b) determine the local (relative) maxima and minima. (e) determine the intervals of concavity. (d) determine the points of inflection. (e) sketch the graph with the above information indicated on the graph.arrow_forwardCan you solve this 2 question numerical methodarrow_forward
- 1. Estimate the area under the graph of f(x)-25-x from x=0 to x=5 using 5 approximating rectangles Using: (A) right endpoints. (B) left endpoints.arrow_forward9. Use fundamental theorem of calculus to find the derivative d a) *dt sin(x) b)(x)√1-2 dtarrow_forward3. Evaluate the definite integral: a) √66x²+8dx b) x dx c) f*(2e* - 2)dx d) √√9-x² e) (2-5x)dx f) cos(x)dx 8)²₁₂√4-x2 h) f7dx i) f² 6xdx j) ²₂(4x+3)dxarrow_forward
- 2. Consider the integral √(2x+1)dx (a) Find the Riemann sum for this integral using right endpoints and n-4. (b) Find the Riemann sum for this same integral, using left endpoints and n=4arrow_forwardProblem 11 (a) A tank is discharging water through an orifice at a depth of T meter below the surface of the water whose area is A m². The following are the values of a for the corresponding values of A: A 1.257 1.390 x 1.50 1.65 1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 Using the formula -3.0 (0.018)T = dx. calculate T, the time in seconds for the level of the water to drop from 3.0 m to 1.5 m above the orifice. (b) The velocity of a train which starts from rest is given by the fol- lowing table, the time being reckoned in minutes from the start and the speed in km/hour: | † (minutes) |2|4 6 8 10 12 14 16 18 20 v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0 Estimate approximately the total distance ran in 20 minutes.arrow_forwardX Solve numerically: = 0,95 In xarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY