   Chapter 10.1, Problem 3CP ### 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 ) =   7   + 3 x   −   x 3 ,  then  f ' ( x )   =   3   −   3 x 2 . Use these functions to decide whether the following statements are true or false.(a) The only critical value is x = 1.(b) The critical points are (1, 0) and (-1, 0).

(a)

To determine

Whether the statement ‘If f(x)=7+3xx3, then f(x)=33x2 then the only critical value is x=1.’ is true or false.

Explanation

Given Information:

The statement ‘If f(x)=7+3xx3, then f(x)=33x2 then the only critical value is x=1.’

Explanation:

Consider the provided equation f(x)=7+3xx3,

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.

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

(b)

To determine

Whether the statement ‘If f(x)=7+3xx3, then f(x)=33x2 then the critical points are (1,0) and (1,0).’ is true or false.

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