19. The graph of f is shown to the right. For which value of x is f'(x) the smallest? [A] x=6 [B] x=-2 [C] x=0 [D] x=2 [E] x=4 £ 2 96 4 2 2 -4- 6
19. The graph of f is shown to the right. For which value of x is f'(x) the smallest? [A] x=6 [B] x=-2 [C] x=0 [D] x=2 [E] x=4 £ 2 96 4 2 2 -4- 6
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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![Transcription for Educational Website:
---
**Question 19:**
The graph of \( f \) is shown to the right.
For which value of \( x \) is \( f'(x) \) the smallest?
Choices:
- [A] \( x = 6 \)
- [B] \( x = -2 \)
- [C] \( x = 0 \)
- [D] \( x = 2 \)
- [E] \( x = 4 \)
**Graph Analysis:**
- The graph depicts a function \( f \) on a set of axes with the x-axis and y-axis marked.
- The curve appears to rise steeply from negative \( y \) values, passes through several critical points where it changes concavity, and ascends again.
- The graph has an inflection point near \( x = 0 \), where it transitions from convex to concave.
- The steepest negative slope, indicating the smallest derivative \( f'(x) \), is likely around \( x = 4 \) as it visually appears to be the point where the graph transitions from descending to ascending with the most pronounced slope.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ef4066a-09c4-44d3-9899-dbf8cf9ac919%2Fe263268e-6a82-4a2b-a8c7-cebf43247148%2Fyjevruc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Transcription for Educational Website:
---
**Question 19:**
The graph of \( f \) is shown to the right.
For which value of \( x \) is \( f'(x) \) the smallest?
Choices:
- [A] \( x = 6 \)
- [B] \( x = -2 \)
- [C] \( x = 0 \)
- [D] \( x = 2 \)
- [E] \( x = 4 \)
**Graph Analysis:**
- The graph depicts a function \( f \) on a set of axes with the x-axis and y-axis marked.
- The curve appears to rise steeply from negative \( y \) values, passes through several critical points where it changes concavity, and ascends again.
- The graph has an inflection point near \( x = 0 \), where it transitions from convex to concave.
- The steepest negative slope, indicating the smallest derivative \( f'(x) \), is likely around \( x = 4 \) as it visually appears to be the point where the graph transitions from descending to ascending with the most pronounced slope.
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