Chapter 1.2, Problem 34E

Solution

To identify: graph the function and intervals on which the function is increasing,

decreasing, or constant.

The function is

Increases: $(-\infty ,-0.549]$

Decreases: $\left[-0.549,1.215\right]$

Increases: $[1.215,\infty )$ .

Given information: 

The function $f\left(x\right)=x^3-x^2-2x$ .

Calculation:

Graph of

  $f\left(x\right)=x^3-x^2-2x$

Let $y=f\left(x\right)$ .

Putting the value of $x=1$ then $y=-2$ .

And $x=-1$ then $y=0$

And $x=-2$ then $y=-16$

And $x=2$ then $y=0$

Plot the graph:

  

Therefore, the function increases in the interval $(-\infty ,-0.549]$ , decreases in the interval $\left[-0.549,1.215\right]$ and increases in the interval $[1.215,\infty )$ .