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The graph of derivative function y = f'(x) is given as föllóws. Answer the questions regarding the original function f (x). 10 (Careful: This is the graph of the derivative!) a) Find the x-coordinates of all critical points of the original function f(x), and determine their nature (local maximum, local minimum, or neither). b) Determine the intervals of increase and decrease for the original function f(x). c) Find the x-coordinates of all inflection points. d) Determine the intervals of concavity for the original function f (x).

The graph of derivative function y = f'(x) is given as föllóws. Answer the questions regarding the original function f (x). 10 (Careful: This is the graph of the derivative!) a) Find the x-coordinates of all critical points of the original function f(x), and determine their nature (local maximum, local minimum, or neither). b) Determine the intervals of increase and decrease for the original function f(x). c) Find the x-coordinates of all inflection points. d) Determine the intervals of concavity for the original function f (x).

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:** This is a graph of the derivative function \( y = f'(x) \). The graph is a curve plotted on a coordinate plane with \( x \)-axis marked from approximately \(-10\) to \(10\) and \( y \)-axis from \(-10\) to \(10\). The curve intersects the \( x \)-axis at various points, creating distinct sections of positive and negative values. --- **Text for Educational Website:** The graph of the derivative function \( y = f'(x) \) is given as follows. Answer the questions regarding the original function \( f(x) \). *(Careful: This is the graph of the derivative!)* a) Find the \( x \)-coordinates of all critical points of the original function \( f(x) \), and determine their nature (local maximum, local minimum, or neither). b) Determine the intervals of increase and decrease for the original function \( f(x) \). c) Find the \( x \)-coordinates of all inflection points. d) Determine the intervals of concavity for the original function \( f(x) \). --- Analyzing the graph, you can locate: - Critical points where \( f'(x) = 0 \) (intersections with the \( x \)-axis). - Intervals of increase and decrease based on the sign of \( f'(x) \). - Inflection points where \( f'(x) \) changes its trend from increasing to decreasing, or vice versa. - Intervals of concavity identified by the behavior of \( f'(x) \).
Transcribed Image Text:**Graph Analysis:** This is a graph of the derivative function \( y = f'(x) \). The graph is a curve plotted on a coordinate plane with \( x \)-axis marked from approximately \(-10\) to \(10\) and \( y \)-axis from \(-10\) to \(10\). The curve intersects the \( x \)-axis at various points, creating distinct sections of positive and negative values. --- **Text for Educational Website:** The graph of the derivative function \( y = f'(x) \) is given as follows. Answer the questions regarding the original function \( f(x) \). *(Careful: This is the graph of the derivative!)* a) Find the \( x \)-coordinates of all critical points of the original function \( f(x) \), and determine their nature (local maximum, local minimum, or neither). b) Determine the intervals of increase and decrease for the original function \( f(x) \). c) Find the \( x \)-coordinates of all inflection points. d) Determine the intervals of concavity for the original function \( f(x) \). --- Analyzing the graph, you can locate: - Critical points where \( f'(x) = 0 \) (intersections with the \( x \)-axis). - Intervals of increase and decrease based on the sign of \( f'(x) \). - Inflection points where \( f'(x) \) changes its trend from increasing to decreasing, or vice versa. - Intervals of concavity identified by the behavior of \( f'(x) \).
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