Chapter 2.3, Problem 26E

a.

To determine

To graph the function using graphing device.

Explanation of Solution

Given information : Use graphing device to graph the function $f\left(x\right)=x^4-16x^2$ .

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $x^4-16x^2$ which is required to graph.

Step 4: Press GRAPH button to graph the function and adjust the windows according to the graph.

The graph is obtained as:

  

Interpretation :

From the above graph, it can be observed that the domain of $f$ is $ℝ$ and the range is $\left[-64,\infty \right)$ .

b.

To determine

To state approximately the interval on which the function is increasing and on which the function is decreasing.

Answer to Problem 26E

The function $f$ is decreasing on $(-\infty ,-2.83]\text{ and }\left[0,2.83\right]$ and increasing on $\left[-2.83,0\right]\text{ and [2}\text{.83,}\infty )$ .

Explanation of Solution

Given information :

The function is $f\left(x\right)=x^4-16x^2$ .

The graph of the function is obtained as:

  

Using $\boxed{\text{TRACE}}$ feature on the calculator, the lowest value is $f\left(-2.83\right)=-64\text{ and }f\left(2.83\right)=-64$ and the highest value is $f\left(0\right)=0$ .

From the above graph, it can be observed that the function $f$ is decreasing on $(-\infty ,-2.83]\text{ and }\left[0,2.83\right]$ and increasing on $\left[-2.83,0\right]\text{ and [2}\text{.83,}\infty )$ .