A function f is continuous on the closed interval [-3,3] such that f(-3) = 4 and f(3) = 1. The function f' and f" have the properties given in the table below. 3. x = 1| 1< x < 3 negative negative -3 < x < -1 x = -1 -1 < x < 1 f'(x) f"(x) fails to exist positive positive negative positive fails to exist a) At what value of x does f have an absolute maximum? Justify your answer. b) What are the x-coordinates of all points of inflection of f on the interval [-3,3]? Justify your answer. c) On the axes provided, sketch a graph that satisfies the given properties of f.

A function f is continuous on the closed interval [-3,3] such that f(-3) = 4 and f(3) = 1. The function f' and f" have the properties given in the table below. 3. x = 1| 1< x < 3 negative negative -3 < x < -1 x = -1 -1 < x < 1 f'(x) f"(x) fails to exist positive positive negative positive fails to exist a) At what value of x does f have an absolute maximum? Justify your answer. b) What are the x-coordinates of all points of inflection of f on the interval [-3,3]? Justify your answer. c) On the axes provided, sketch a graph that satisfies the given properties of f.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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