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(d) Estimate the x-values of the inflection points of f. (e) On what intervals is f concave up? concave down? (f) Using the information above and assuming that f (0) = -2, sketch a graph of f on top of the graph of f' below. %3D -1 3 4 -2 -3 -4 1.

(d) Estimate the x-values of the inflection points of f. (e) On what intervals is f concave up? concave down? (f) Using the information above and assuming that f (0) = -2, sketch a graph of f on top of the graph of f' below. %3D -1 3 4 -2 -3 -4 1.

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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**8. Below is a graph of \( f' \) (DERIVATIVE). Assume that the domain is all real numbers.** --- **Graph Explanation:** - **Axes:** - The horizontal axis (x-axis) ranges from \(-1\) to \(4\). - The vertical axis (y-axis) ranges from \(-4\) to \(2\). - **Curve Details:** - The graph represents a smooth curve of the derivative \( f' \). - The curve intersects the y-axis above the point \(1\), indicating that \( f’(0) \) is positive. - It crosses the x-axis near \(x = 0.5\), suggesting a critical point. - It reaches a local maximum above \(x = 1\). - The graph then descends, crossing the x-axis just after \(x = 2\). - It continues downward, reaching a local minimum near \(x = 3\) before rising back towards the x-axis. This graph is used to analyze the behavior of the function \( f \) by examining the qualities of its derivative \( f' \). Understanding this graph helps in identifying intervals of increase or decrease in \( f \), as well as locating critical points and inflection points.
Transcribed Image Text:**8. Below is a graph of \( f' \) (DERIVATIVE). Assume that the domain is all real numbers.** --- **Graph Explanation:** - **Axes:** - The horizontal axis (x-axis) ranges from \(-1\) to \(4\). - The vertical axis (y-axis) ranges from \(-4\) to \(2\). - **Curve Details:** - The graph represents a smooth curve of the derivative \( f' \). - The curve intersects the y-axis above the point \(1\), indicating that \( f’(0) \) is positive. - It crosses the x-axis near \(x = 0.5\), suggesting a critical point. - It reaches a local maximum above \(x = 1\). - The graph then descends, crossing the x-axis just after \(x = 2\). - It continues downward, reaching a local minimum near \(x = 3\) before rising back towards the x-axis. This graph is used to analyze the behavior of the function \( f \) by examining the qualities of its derivative \( f' \). Understanding this graph helps in identifying intervals of increase or decrease in \( f \), as well as locating critical points and inflection points.
(d) Estimate the x-values of the inflection points of \( f \). (e) On what intervals is \( f \) concave up? concave down? (f) Using the information above and assuming that \( f(0) = -2 \), sketch a graph of \( f \) on top of the graph of \( f'' \) below. **Graph Explanation:** The graph shown is of \( f'' \) (the second derivative of \( f \)). It features a curve plotted against the x-axis ranging from approximately -1 to 4. Key features include: - A crossing of the x-axis at around \( x = 0 \) and \( x = 2.5 \). - The graph is above the x-axis around \( x = 0 \) to \( x = 2.5 \), indicating intervals where \( f \) is concave up. - The graph dips below the x-axis approximately beyond \( x = 2.5 \), indicating an interval where \( f \) is concave down. These characteristics will help identify the intervals of concavity and estimate the inflection points for the function \( f \).
Transcribed Image Text:(d) Estimate the x-values of the inflection points of \( f \). (e) On what intervals is \( f \) concave up? concave down? (f) Using the information above and assuming that \( f(0) = -2 \), sketch a graph of \( f \) on top of the graph of \( f'' \) below. **Graph Explanation:** The graph shown is of \( f'' \) (the second derivative of \( f \)). It features a curve plotted against the x-axis ranging from approximately -1 to 4. Key features include: - A crossing of the x-axis at around \( x = 0 \) and \( x = 2.5 \). - The graph is above the x-axis around \( x = 0 \) to \( x = 2.5 \), indicating intervals where \( f \) is concave up. - The graph dips below the x-axis approximately beyond \( x = 2.5 \), indicating an interval where \( f \) is concave down. These characteristics will help identify the intervals of concavity and estimate the inflection points for the function \( f \).
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