For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality 4 x − 5 = 3 x − 2
For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality 4 x − 5 = 3 x − 2
Solution Summary: The author explains that the given equation is an absolute value equation, where k is any positive real number.
a. Identify the type of equation or inequality (some may fit more than one category).
b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible.
• Linear equation or inequality
• Quadratic equation
• Rational equation
• Absolute value equation or inequality
• Radical equation
• Equation in quadratic form
• Polynomial equation
degree
>
2
• Compound inequality
4
x
−
5
=
3
x
−
2
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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.