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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

In Problems 27 and 28, f ' ( x ) and its graph are given.

(a) Use the graph of f ' ( x ) to determine (estimate) where the graph of f ( x ) is increasing, where it is decreasing, and where it has relative extrema.

(b) Use the graph of f ' ( x ) to determine where f " ( x )

> 0, where f " ( x )

< 0, and where f " ( x )

= 0.

(c) Verify that the given f ( x )

has f ' ( x ) as its derivative, and graph f ( x ) to check your conclusions in

part (a).

(d) Calculate f " ( x ) and graph it to check your conclusions in part (b).

f ' ( x ) = 6 x 2 x 3 ( for  f ( x ) = 2 x 3 x 4 4 )

Chapter 10, Problem 28RE,  In Problems 27 and 28,  and its graph are given.
(a) Use the graph of  to determine (estimate)

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f(x)=6x2x3.

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 10, Problem 28RE , additional homework tip  1

Explanation

Given Information:

The provided graph of the function f(x)=6x2x3 is,

Explanation:

Consider the provided graph of the function f(x)=6x2x3,

Since, the graph is of the function f(x).

Recall that the graph of a function is increasing if first derivative of the function is positive and decreasing if the first derivative is negative

(b)

To determine

To calculate: The region where f(x)>0, f(x)<0 and f(x)=0 in the graph of the function f(x)=6x2x3.

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 10, Problem 28RE , additional homework tip  2

(c)

To determine

To prove: The derivative f(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

(d)

To determine

To calculate: The function f(x) for the function f(x)=2x3x44 and check the conclusion from part (b) by draw the graph of f(x).

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