Let g(x) = x – 5x. Find the exact value of I where g'(x) = 0. 1, Let r(t) = t - 12t. Find the exact values of t where r' (t) = 0. Enter your answer as a list separated %3D by commas.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Here's a quick example of the process we'll need to follow. Lets say we want to know the values of x
where the derivative of f(x) = x° - 3x is zero. First, we find the derivative. Using the shortcut
3x-3. So the equation we need
to solve is 3x? - 3 = 0. If we divide both sides of this equation by 3, we get r² – 1 = 0. Now, this is a
quadratic equation, and it has two solutions. There are several ways to find both solutions. One way
would be to factor the equation, giving us (x + 1)(x – 1) = 0, from which we can see that the
-1 and x = 1. (An alterative method for finding the solutions might be to use the
formulas from Section 9.4, we can see that the derivative is f'(x) =
2
%3D
solutions are x =
Quadratic Formula.)
So, the derivative of f(x) = x° - 3x is zero when x
1, 1 (which we read aloud as "x equals -1 or
1").
Let g(æ) = x² – 5x. Find the exact value of x where g'(x) = 0.
Let r(t) = t° – 12t. Find the exact values of t where r'(t) = 0. Enter your answer as a list separated
%3D
by commas.
Transcribed Image Text:Here's a quick example of the process we'll need to follow. Lets say we want to know the values of x where the derivative of f(x) = x° - 3x is zero. First, we find the derivative. Using the shortcut 3x-3. So the equation we need to solve is 3x? - 3 = 0. If we divide both sides of this equation by 3, we get r² – 1 = 0. Now, this is a quadratic equation, and it has two solutions. There are several ways to find both solutions. One way would be to factor the equation, giving us (x + 1)(x – 1) = 0, from which we can see that the -1 and x = 1. (An alterative method for finding the solutions might be to use the formulas from Section 9.4, we can see that the derivative is f'(x) = 2 %3D solutions are x = Quadratic Formula.) So, the derivative of f(x) = x° - 3x is zero when x 1, 1 (which we read aloud as "x equals -1 or 1"). Let g(æ) = x² – 5x. Find the exact value of x where g'(x) = 0. Let r(t) = t° – 12t. Find the exact values of t where r'(t) = 0. Enter your answer as a list separated %3D by commas.
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