Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

Question

use a graphing utility to graph the function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

f (x) = x³ - 3x + 2   (-2, 2)

Answer 1

Step 1 :

The graph of the function on the interval :

Step 2 :

 A function has a relative(or local) maximum at , if .

 A function has a relative(or local) minimum at , if .

Observe the graph,

Since , has a local maximum at .

The local maximum is .

Since , has a local minimum at .

The local minimum is .

Step 3 :

The function is increasing for all values of between to and to .

The function is increasing over the intervals and .

The function is decreasing for all values of between and .

The function is decreasing over the interval .

Solution :

Local maximum is .

Local minimum is .

The function increasing over the intervals and .

The function decreasing over the interval .