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Chapter 3: Q. 13 (page 176)

Approximate the local maximum values and local minimum values of f(x)=x3-5x+1 on (-4,4). Determine where the function is increasing and where it is decreasing.

Short Answer

Expert verified

The graph of the function over the given interval is given as

For the function, the local maximum value is 5.3and it occurs at x=-1.3.

The local minimum value is -3.3and it occurs at x=1.3.

The graph is increasing over the interval -4,-1.3and1.3,4and it is decreasing over the interval -1.3,1.3.

Step by step solution

01

Step 1. Given information.

The given function isf(x)=x3-5x+1.

02

Step 2. Graph the function.

Using a graphing utility the graph of the functionf(x)=x3-5x+1over the interval -4,4is given as

03

Step 3. Local maximum and minimum value. 

The function has a local maximum at-1.3, since for allxclose to -1.3, we have f(x)鈮�-1.3. The local maximum value is f(-1.3)=5.3.

The function has a local minimum at 1.3and the local minimum value is f(1.3)=-3.3.

04

Step 4. Increasing and Decreasing interval.

From the graph, it can be seen that the graph is increasing in the interval -4,-1.3and1.3,4.

And the graph is decreasing in the intervals -1.3,1.3.

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