The graph below is the graph of the First Derivative of f(x)... that is it is the graph of f '(*). Five (5) different points are labeled on the graph. B Do ane (and onfon)of Otherwise the mane (A) A (1) D (H)Evalu Which point or points (if any) represent critical numbers for the function f (x) ? Which point or points (if any) represent local maximums for the function f (x)? Which point or points (if any) represent local minimums for the function f (x)? Which point or points (if any) represent points of inflection for the function f (x)?

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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**Graph Description:**

The graph depicted is of the first derivative of a function \( f(x) \), labeled as \( f'(x) \). Five distinct points are marked on this graph: A, B, C, D, and E. The graph appears to be a quadratic function, beginning and ending above the x-axis with a vertex below it. 

- **Point A** is on the x-axis (where \( f'(x) = 0 \)).
- **Point B** is a peak on the graph.
- **Point C** lies on the x-axis between points B and D (another instance where \( f'(x) = 0 \)).
- **Point D** is at the vertex, below the x-axis.
- **Point E** is another intersection with the x-axis (where \( f'(x) = 0 \)).

**Questions:**

- Which point or points (if any) represent critical numbers for the function \( f(x) \)?

- Which point or points (if any) represent local maximums for the function \( f(x) \)?

- Which point or points (if any) represent local minimums for the function \( f(x) \)?

- Which point or points (if any) represent points of inflection for the function \( f(x) \)?
Transcribed Image Text:**Graph Description:** The graph depicted is of the first derivative of a function \( f(x) \), labeled as \( f'(x) \). Five distinct points are marked on this graph: A, B, C, D, and E. The graph appears to be a quadratic function, beginning and ending above the x-axis with a vertex below it. - **Point A** is on the x-axis (where \( f'(x) = 0 \)). - **Point B** is a peak on the graph. - **Point C** lies on the x-axis between points B and D (another instance where \( f'(x) = 0 \)). - **Point D** is at the vertex, below the x-axis. - **Point E** is another intersection with the x-axis (where \( f'(x) = 0 \)). **Questions:** - Which point or points (if any) represent critical numbers for the function \( f(x) \)? - Which point or points (if any) represent local maximums for the function \( f(x) \)? - Which point or points (if any) represent local minimums for the function \( f(x) \)? - Which point or points (if any) represent points of inflection for the function \( f(x) \)?
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