Chapter 2, Problem 22RE

In Problems 22 and 23, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing.

$f\left(x\right)=2x^3-5x+1\left[-3,3\right]$

To determine

To graph:

a. $f\left(x\right)=2x^3-5x+1$ using graphing utility.

Answer to Problem 22RE

Solution:

a.

Explanation of Solution

Given:

$f\left(x\right)=2x^3-5x+1$; $\left[-3,3\right]$

Graph:

a. Graph of $f\left(x\right)=2x^3-5x+1$ using graphing utility.

Interpretation:

a. The graph of $f\left(x\right)=2x^3-5x+1$ is plotted using graphing utility.

To determine

To graph:

b. Approximate local maximum values and local minimum values.

Answer to Problem 22RE

Solution:

b. Local maximum values: $\left(-0.913,4.043\right)$.

Local minimum values: $\left(0.913,-2.043\right)$.

Explanation of Solution

Given:

$f\left(x\right)=2x^3-5x+1$; $\left[-3,3\right]$

Interpretation:

b. From the graph we see that,

Local maximum values: $\left(-0.913,4.043\right)$.

Local minimum values: $\left(0.913,-2.043\right)$.

To determine

To graph:

c. Where the function is increasing and where it is decreasing.

Answer to Problem 22RE

Solution:

c. The function is increasing in the interval $\left(-3,-0.913\right)\cup \left(0.913,3\right)$ as the function is defined in the interval $\left[-3,3\right]$.

The function is decreasing in the interval $(-0.913,0.913)$.

Explanation of Solution

Given:

$f\left(x\right)=2x^3-5x+1$; $\left[-3,3\right]$

Interpretation:

c. From the graph, we see that,

The function is increasing in the interval $\left(-3,-0.913\right)\cup \left(0.913,3\right)$ as the function is defined in the interval $\left[-3,3\right]$.

The function is decreasing in the interval $(-0.913,0.913)$.