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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![**Problem**
Given the function \( f(x) = (2x - 1)(4x + 5) \), answer the following questions:
a. Compute \( f(-1) = \) [__________]
b. Compute \( f'(-1) = \) [__________]
c. Compute \( f''(-1) = \) [__________]
d. Find the values of \( x \) for which \( f(x) = 0 \). [__________], [__________]
e. Find the values of \( x \) for which \( f'(x) = 0 \). [__________]
**Instructions**
- For part (a), substitute \(-1\) into the function \( f(x) \).
- For part (b), first find the derivative \( f'(x) \), and then substitute \(-1\).
- For part (c), compute the second derivative \( f''(x) \), and then substitute \(-1\).
- For part (d), solve \( f(x) = 0 \) for \( x \).
- For part (e), solve \( f'(x) = 0 \) for \( x \).
Please begin solving the equations and filling in the blanks.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb712a4a5-b39c-49c8-b724-4a3b4fedc327%2F3e2a8701-f4ae-48e9-a770-ffd8c40db4b6%2Fobn81zm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem**
Given the function \( f(x) = (2x - 1)(4x + 5) \), answer the following questions:
a. Compute \( f(-1) = \) [__________]
b. Compute \( f'(-1) = \) [__________]
c. Compute \( f''(-1) = \) [__________]
d. Find the values of \( x \) for which \( f(x) = 0 \). [__________], [__________]
e. Find the values of \( x \) for which \( f'(x) = 0 \). [__________]
**Instructions**
- For part (a), substitute \(-1\) into the function \( f(x) \).
- For part (b), first find the derivative \( f'(x) \), and then substitute \(-1\).
- For part (c), compute the second derivative \( f''(x) \), and then substitute \(-1\).
- For part (d), solve \( f(x) = 0 \) for \( x \).
- For part (e), solve \( f'(x) = 0 \) for \( x \).
Please begin solving the equations and filling in the blanks.
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