   Chapter 10.1, Problem 4CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If f ‘ ( x ) has the following partial sign diagram, make a “stick-figure sketch of f ( x ) and label where any maxima and minima occur. Assume that f ( x ) is defined for all real numbers. To determine

The “stick-figure” sketch of f(x) if f'(x) has the following sign diagram and label the maxima and minima where it may occur. Explanation

Given Information:

The sign diagram of f'(x) is as follows:

Explanation:

Consider the provided sign diagram,

The diagram shows that,

It is increasing at x<1 and x>0.

It is decreasing at 1<x<0.

It is not defined at x=0.

The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value.

Hence, there will no change in the values of critical values as in the derivative graph.

The critical points in this case are,

1,0,2.

The stick diagram helps in identifying the relative maxima and minima

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