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The graph of f'(æ) ,the derivative of f(æ), is shown below. Find the critical number(s) of f(x). -3 -2 -1 1 2 3 -1 -2 -3 -5 -6 -7 -8 a) Oz = -1 b) Or = {-1,1} c) Or = 0 d) Or = {-1,0, 1} e) Ox = 1

The graph of f'(æ) ,the derivative of f(æ), is shown below. Find the critical number(s) of f(x). -3 -2 -1 1 2 3 -1 -2 -3 -5 -6 -7 -8 a) Oz = -1 b) Or = {-1,1} c) Or = 0 d) Or = {-1,0, 1} e) Ox = 1

Calculus: Early Transcendentals
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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**Educational Content: Finding Critical Numbers** **Problem Statement:** The graph of \( f'(x) \), the derivative of \( f(x) \), is shown below. Find the critical number(s) of \( f(x) \). **Graph Analysis:** The graph depicts a parabola opening downwards. The x-axis ranges from -3 to 3, and the y-axis ranges from -8 to 2. Critical numbers occur where the derivative \( f'(x) \) is zero, indicating potential maxima, minima, or points of inflection. In this graph, the parabola intersects the x-axis at \( x = -1 \) and \( x = 1 \). **Options:** a) \( x = -1 \) b) \( x = \{-1, 1\} \) c) \( x = 0 \) d) \( x = \{-1, 0, 1\} \) e) \( x = 1 \) **Answer:** The critical numbers are the x-values where the derivative \( f'(x) = 0 \), which happen at the x-intercepts of the graph. Therefore, the correct choice is: b) \( x = \{-1, 1\} \)
Transcribed Image Text:**Educational Content: Finding Critical Numbers** **Problem Statement:** The graph of \( f'(x) \), the derivative of \( f(x) \), is shown below. Find the critical number(s) of \( f(x) \). **Graph Analysis:** The graph depicts a parabola opening downwards. The x-axis ranges from -3 to 3, and the y-axis ranges from -8 to 2. Critical numbers occur where the derivative \( f'(x) \) is zero, indicating potential maxima, minima, or points of inflection. In this graph, the parabola intersects the x-axis at \( x = -1 \) and \( x = 1 \). **Options:** a) \( x = -1 \) b) \( x = \{-1, 1\} \) c) \( x = 0 \) d) \( x = \{-1, 0, 1\} \) e) \( x = 1 \) **Answer:** The critical numbers are the x-values where the derivative \( f'(x) = 0 \), which happen at the x-intercepts of the graph. Therefore, the correct choice is: b) \( x = \{-1, 1\} \)
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