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Given the graph of f(x) below, find the graph of the derivative of f(x). -7-6-5-4-3-2-1 4 567

Given the graph of f(x) below, find the graph of the derivative of f(x). -7-6-5-4-3-2-1 4 567

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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Question 8
The image presents a problem that involves analyzing a graph and finding the derivative. The task is stated as follows: "Given the graph of \( f(x) \) below, find the graph of the derivative of \( f(x) \)." ### Graph Description: - **Axes and Grid**: The graph contains a set of axes with a grid superimposed, providing a clear coordinate system. The x-axis ranges from -7 to 7, and the y-axis ranges from -7 to 7. - **Plot**: The function \( f(x) \) is depicted as a series of line segments creating angular points, suggesting a piecewise linear function. ### Characteristics of the Graph: - **Line Segments**: The function appears to have three distinct line segments: - From the point (-3, 4), the line slopes down sharply through (0, -3) to (1, -3). - The line then ascends rapidly to (2, 7). - Finally, the line descends equally sharply back down to point (4, -7). ### Interpretation for Derivative: - **Derivative Behavior**: Since the function is piecewise linear, the derivative will be constant over the intervals defined by the line segments. - Each segment’s slope will become the value of the derivative within that interval. This problem requires calculating these slopes to graph \( f'(x) \), the derivative of \( f(x) \).
Transcribed Image Text:The image presents a problem that involves analyzing a graph and finding the derivative. The task is stated as follows: "Given the graph of \( f(x) \) below, find the graph of the derivative of \( f(x) \)." ### Graph Description: - **Axes and Grid**: The graph contains a set of axes with a grid superimposed, providing a clear coordinate system. The x-axis ranges from -7 to 7, and the y-axis ranges from -7 to 7. - **Plot**: The function \( f(x) \) is depicted as a series of line segments creating angular points, suggesting a piecewise linear function. ### Characteristics of the Graph: - **Line Segments**: The function appears to have three distinct line segments: - From the point (-3, 4), the line slopes down sharply through (0, -3) to (1, -3). - The line then ascends rapidly to (2, 7). - Finally, the line descends equally sharply back down to point (4, -7). ### Interpretation for Derivative: - **Derivative Behavior**: Since the function is piecewise linear, the derivative will be constant over the intervals defined by the line segments. - Each segment’s slope will become the value of the derivative within that interval. This problem requires calculating these slopes to graph \( f'(x) \), the derivative of \( f(x) \).
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