Chapter 2, Problem 55RE

To determine

Find the interval of increasing and decreasing of the given function $f\left(x\right)=\left|x^4-16\right|$ by using T1-83 calculator.

Answer to Problem 55RE

The graph is increasing on $\left[-2,0\right],\left[2,\infty \right)$ and decreasing on $\left(-\infty ,2\right],\left[0,2\right]$

Explanation of Solution

Given information: consider the function $f\left(x\right)=\left|x^4-16\right|$

Calculation:

Press the $\boxed{Y=}$ button and enter the function $\left(\left(\text{X^4}\right)\text{-16}\right).$

  

Once this is done on the Window screen

X min =5

X max= 5

Y min = -5

Y max= 20

Adjust Xscl =1

This gives a rang that is good for many

Varied graph types

Set the window

  

Then click the GRAPH button.

  

For finding increase and decrease intervals, click the TRACE button and use the left and right buttons to find values.

So the graph is increase on $-2to\text{ 0}$ , $2\text{ to }\infty$ and decrease on $-\infty \text{ to }-2$ , $0\text{ to 2}$ .

  

Thus, the graph is increasing on $\left[-2,0\right],\left[2,\infty \right)$ and decreasing on $\left(-\infty ,2\right],\left[0,2\right]$