Explanation Given information: At exactly two of the labeled point in the given figure, the derivative f ' is 0; the second derivative f ' ' is not zero at any of the labeled points. The given graph is Calculation: The term f ( x ) represents the value of y for the given value of x. The term f ' ( x ) represents the first order derivative i.e. slope of the graph at the given point. The term f ' ' ( x ) is the second order derivative which is negative when the curve is concave down and positive when it is concave up and zero at the point of inflection i.e. where the curve changes it concavity. At the point A , Since the point A lies below the x axis hence f is negative. Since the tangent at the point A is horizontal hence f ' is zero. And since the graph is concave down at A therefore f ' ' is negative. At the point B , Since the point B lies above the x axis hence f is positive. Since the tangent at the point B is horizontal hence f ' is zero. And since the graph is concave up at B therefore f ' ' is positive

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 2.4, Problem 23P

To determine

To fill:

The table shown below with the signs of f,f',f'' at each marked point on the graph.

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Chapter 2.4, Problem 22P

Chapter 2.4, Problem 24P

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Chapter 2 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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The table shown below with the signs of f , f ' , f ' ' at each marked point on the graph.

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To fill: The table shown below with the signs of f,f',f'' at each marked point on the graph.

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Chapter 2 Solutions

To fill:

The table shown below with the signs of f,f',f'' at each marked point on the graph.