Please explain how to solve. **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.

Answered: Image /qna-images/answer/e00ba457-a172-49cd-ba85-2ecf88d5eeb2.jpg

Answered: Use the graph of f '(x) shown to…

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

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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