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Based on the graph of g"(x) pictured above, how many points of inflection exist for the twice differentiable function g(x) on the interval -4

Based on the graph of g"(x) pictured above, how many points of inflection exist for the twice differentiable function g(x) on the interval -4

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:** Based on the graph of \( g''(x) \) pictured above, how many points of inflection exist for the twice differentiable function \( g(x) \) on the interval \(-4 < x < 8\)? **Graph Explanation:** The graph depicts a continuous curve of the function \( g''(x) \) over the x-axis range from \(-4\) to \(8\). The curve crosses the x-axis several times, indicating potential points of inflection for \( g(x) \). The curve starts below the x-axis at \( x = -4 \), crosses the x-axis upwards at a point between \( x = -2 \) and \( x = -1 \), goes above the x-axis and crosses back down between \( x = 1 \) and \( x = 2 \), rises again to cross upwards around \( x = 4 \), and crosses down once more shortly after \( x = 6 \). **Multiple Choice Options:** - a. 2 - b. 4 - c. 1 - d. 3 **Instructions:** Select one of the options based on the analysis of the graph. A point of inflection occurs where the second derivative \( g''(x) \) changes sign, indicating a change in the concavity of the original function \( g(x) \). **Submit Answer:** Click “Check” to verify your answer. **Explanation:** To determine the number of inflection points, count how many times the curve crosses the x-axis within the interval. Each crossing signifies a potential change in the concavity of \( g(x) \). **Next Page**
Transcribed Image Text:**Question:** Based on the graph of \( g''(x) \) pictured above, how many points of inflection exist for the twice differentiable function \( g(x) \) on the interval \(-4 < x < 8\)? **Graph Explanation:** The graph depicts a continuous curve of the function \( g''(x) \) over the x-axis range from \(-4\) to \(8\). The curve crosses the x-axis several times, indicating potential points of inflection for \( g(x) \). The curve starts below the x-axis at \( x = -4 \), crosses the x-axis upwards at a point between \( x = -2 \) and \( x = -1 \), goes above the x-axis and crosses back down between \( x = 1 \) and \( x = 2 \), rises again to cross upwards around \( x = 4 \), and crosses down once more shortly after \( x = 6 \). **Multiple Choice Options:** - a. 2 - b. 4 - c. 1 - d. 3 **Instructions:** Select one of the options based on the analysis of the graph. A point of inflection occurs where the second derivative \( g''(x) \) changes sign, indicating a change in the concavity of the original function \( g(x) \). **Submit Answer:** Click “Check” to verify your answer. **Explanation:** To determine the number of inflection points, count how many times the curve crosses the x-axis within the interval. Each crossing signifies a potential change in the concavity of \( g(x) \). **Next Page**
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