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If the figure below is the graph of the derivativef', answer the following: Where do the points of inflection of f occur?

If the figure below is the graph of the derivativef', answer the following: Where do the points of inflection of f occur?

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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**Graph Analysis: Cubic Function** This graph represents a cubic function plotted with an x-axis ranging from approximately -2 to 18 and a y-axis ranging from -4 to 4. **Key Features:** 1. **Plot Description:** - The curve starts at a high point on the left, approaching y = 3.5 when x = -2. - It then descends slightly, reaching y = 3 at x = 2, before climbing again to a peak at y = 3.8 around x = 3. - A rapid descent follows, passing through the x-axis near x = 5. - The curve continues declining to a minimum point below the x-axis near y = -3.5 at x = 9. - Following the minimum, the graph rises again; it intersects the x-axis at x = 14 before leveling off at y = 2 as x approaches 18. 2. **Critical Points:** - **Local Maximum:** Near (3, 3.8) - **X-Intercepts:** Approximate x-intercepts at (5, 0) and (14, 0) - **Local Minimum:** Near (9, -3.5) 3. **Axes:** - **X-axis:** Represents the domain from approximately -2 to 18. - **Y-axis:** Represents the range from -4 to 4. 4. **Behavior:** - The graph demonstrates typical cubic function behavior with inflection points and changes in direction. - It crosses the x-axis twice, indicating two real roots. This graph illustrates how cubic functions can model various scenarios with their characteristic "S" shaped curves and turning points. Such functions are frequently used in physics and engineering to model non-linear relationships.
Transcribed Image Text:**Graph Analysis: Cubic Function** This graph represents a cubic function plotted with an x-axis ranging from approximately -2 to 18 and a y-axis ranging from -4 to 4. **Key Features:** 1. **Plot Description:** - The curve starts at a high point on the left, approaching y = 3.5 when x = -2. - It then descends slightly, reaching y = 3 at x = 2, before climbing again to a peak at y = 3.8 around x = 3. - A rapid descent follows, passing through the x-axis near x = 5. - The curve continues declining to a minimum point below the x-axis near y = -3.5 at x = 9. - Following the minimum, the graph rises again; it intersects the x-axis at x = 14 before leveling off at y = 2 as x approaches 18. 2. **Critical Points:** - **Local Maximum:** Near (3, 3.8) - **X-Intercepts:** Approximate x-intercepts at (5, 0) and (14, 0) - **Local Minimum:** Near (9, -3.5) 3. **Axes:** - **X-axis:** Represents the domain from approximately -2 to 18. - **Y-axis:** Represents the range from -4 to 4. 4. **Behavior:** - The graph demonstrates typical cubic function behavior with inflection points and changes in direction. - It crosses the x-axis twice, indicating two real roots. This graph illustrates how cubic functions can model various scenarios with their characteristic "S" shaped curves and turning points. Such functions are frequently used in physics and engineering to model non-linear relationships.
**Problem Statement:** If the figure below is the graph of the derivative \( f' \), answer the following: 1. Where do the points of inflection of \( f \) occur? [Input Box] 2. On which interval(s) is \( f \) concave down? [Input Box] **Graph Explanation:** The graph shown is the derivative \( f' \) of a function \( f \). It is a continuous curve with changes in direction, crossing the x-axis and having local maxima and minima. - The x-axis intercepts indicate potential points of inflection for the function \( f \). - The intervals where \( f' \) is negative suggest regions where the function \( f \) is concave down.
Transcribed Image Text:**Problem Statement:** If the figure below is the graph of the derivative \( f' \), answer the following: 1. Where do the points of inflection of \( f \) occur? [Input Box] 2. On which interval(s) is \( f \) concave down? [Input Box] **Graph Explanation:** The graph shown is the derivative \( f' \) of a function \( f \). It is a continuous curve with changes in direction, crossing the x-axis and having local maxima and minima. - The x-axis intercepts indicate potential points of inflection for the function \( f \). - The intervals where \( f' \) is negative suggest regions where the function \( f \) is concave down.
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