Consider the graph of f. 5 1 + 1 2 3 4 5 6 7 8. 9. Determine the correct statement(s) about f'(x). O f'(0.5) > f' (3.5) O s'(7.5) = f'(2.5) O f'(3.5) = f'(0.5) ロf(7.5) > f'(6.5) O f'(0.5) < f'(3.5) ロf(7.5)
Consider the graph of f. 5 1 + 1 2 3 4 5 6 7 8. 9. Determine the correct statement(s) about f'(x). O f'(0.5) > f' (3.5) O s'(7.5) = f'(2.5) O f'(3.5) = f'(0.5) ロf(7.5) > f'(6.5) O f'(0.5) < f'(3.5) ロf(7.5)
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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![**Consider the graph of \( f \).**
*Graph Description:*
- The graph of the function \( f(x) \) is plotted on the coordinate plane with \( x \)-axis ranging from 0 to 9 and \( y \)-axis ranging from 1 to 5.
- The graph starts near the point (0, 1) and increases slightly until \( x = 3 \).
- From \( x = 3 \) to \( x = 6 \), the graph rises more sharply, peaking at around \( y = 4.5 \).
- From \( x = 6 \) to \( x = 9 \), the graph declines slightly, ending at a point where \( y \) is approximately 3.
**Determine the correct statement(s) about \( f'(x) \).**
- [ ] \( f'(0.5) > f'(3.5) \)
- [ ] \( f'(7.5) = f'(2.5) \)
- [ ] \( f'(3.5) = f'(0.5) \)
- [ ] \( f'(7.5) > f'(6.5) \)
- [ ] \( f'(0.5) < f'(3.5) \)
- [ ] \( f'(7.5) < f'(6.5) \)
- [ ] \( f'(8.5) < f'(2.5) \)
**Explanation:**
The statements above ask us to compare the derivatives (slopes) of the function at different points. \( f'(x) \) represents the slope of the tangent to the curve at each point \( x \). The task is to determine which relationships among these derivatives are true based on the given graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07bee885-b193-43d8-ac2a-8488a7e88bc2%2F14edfd65-c379-4630-ba2b-59cee151b89a%2F6cqnyl8_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the graph of \( f \).**
*Graph Description:*
- The graph of the function \( f(x) \) is plotted on the coordinate plane with \( x \)-axis ranging from 0 to 9 and \( y \)-axis ranging from 1 to 5.
- The graph starts near the point (0, 1) and increases slightly until \( x = 3 \).
- From \( x = 3 \) to \( x = 6 \), the graph rises more sharply, peaking at around \( y = 4.5 \).
- From \( x = 6 \) to \( x = 9 \), the graph declines slightly, ending at a point where \( y \) is approximately 3.
**Determine the correct statement(s) about \( f'(x) \).**
- [ ] \( f'(0.5) > f'(3.5) \)
- [ ] \( f'(7.5) = f'(2.5) \)
- [ ] \( f'(3.5) = f'(0.5) \)
- [ ] \( f'(7.5) > f'(6.5) \)
- [ ] \( f'(0.5) < f'(3.5) \)
- [ ] \( f'(7.5) < f'(6.5) \)
- [ ] \( f'(8.5) < f'(2.5) \)
**Explanation:**
The statements above ask us to compare the derivatives (slopes) of the function at different points. \( f'(x) \) represents the slope of the tangent to the curve at each point \( x \). The task is to determine which relationships among these derivatives are true based on the given graph.
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