   Chapter 10, Problem 28RE ### 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

# 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 inpart (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 ) (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. 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. (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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