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Use the graph of f '(x) shown to identify a possible graph of f(x). 80- 40 -10 10 -40- -80- AY 80 80+ 40 40 -10 -10 10 -40- -40 -80+ -80+ 80 80 40 40 -10 -5 10 -10 10 40- 40+ -80 -80

Use the graph of f '(x) shown to identify a possible graph of f(x). 80- 40 -10 10 -40- -80- AY 80 80+ 40 40 -10 -10 10 -40- -40 -80+ -80+ 80 80 40 40 -10 -5 10 -10 10 40- 40+ -80 -80

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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**Title: Exploring Derivative Graphs** **Introduction:** In this exercise, you'll explore how the graph of a derivative, \( f'(x) \), corresponds to potential graphs of the original function, \( f(x) \). **Primary Graph:** The main graph displays \( f'(x) \), depicted in red. It features the following characteristics: - A vertical asymptote at \( x = 0 \). - The graph approaches positive infinity as \( x \) approaches 0 from the right. - The graph approaches negative infinity as \( x \) approaches 0 from the left. **Potential Function Graphs:** Below are four graphs (in different colors) representing possible shapes of \( f(x) \). The task is to identify the one that matches the behavior of \( f'(x) \). 1. **Graph A (Green):** - Horizontal axis intercepts and undefined regions align with \( f'(x) \). 2. **Graph B (Blue):** - Exhibits symmetry and visible curvature changes at \( x = 0 \). 3. **Graph C (Yellow):** - S-shaped curve with a distinct point of inflection beyond \( x = 0 \). 4. **Graph D (Purple):** - Displays a steep change resembling a cusp or corner near \( x = 0 \). **Conclusion:** Analyze each potential function graph by examining critical points, asymptotic behavior, and curvature. Select the graph consistent with the derivative properties presented. This exercise enhances understanding of the relationship between a function and its derivative.
Transcribed Image Text:**Title: Exploring Derivative Graphs** **Introduction:** In this exercise, you'll explore how the graph of a derivative, \( f'(x) \), corresponds to potential graphs of the original function, \( f(x) \). **Primary Graph:** The main graph displays \( f'(x) \), depicted in red. It features the following characteristics: - A vertical asymptote at \( x = 0 \). - The graph approaches positive infinity as \( x \) approaches 0 from the right. - The graph approaches negative infinity as \( x \) approaches 0 from the left. **Potential Function Graphs:** Below are four graphs (in different colors) representing possible shapes of \( f(x) \). The task is to identify the one that matches the behavior of \( f'(x) \). 1. **Graph A (Green):** - Horizontal axis intercepts and undefined regions align with \( f'(x) \). 2. **Graph B (Blue):** - Exhibits symmetry and visible curvature changes at \( x = 0 \). 3. **Graph C (Yellow):** - S-shaped curve with a distinct point of inflection beyond \( x = 0 \). 4. **Graph D (Purple):** - Displays a steep change resembling a cusp or corner near \( x = 0 \). **Conclusion:** Analyze each potential function graph by examining critical points, asymptotic behavior, and curvature. Select the graph consistent with the derivative properties presented. This exercise enhances understanding of the relationship between a function and its derivative.
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