Chapter 3.2, Problem 68E

To determine

To graph and compare the each function.

Explanation of Solution

Given information: the functionis $y=\frac{1}{3}{x}^7-17x^2+7$ .

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 $\text{Y=}\frac{1}{3}{x}^7-17x^2+7$ which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

There appears to be one local maxima on the axis $x=0$ ,and one minima between theaxis $x=1$ and $x=2$ . Using the $\boxed{\text{TRACE}}$ feature on the graphing device, move the cursor along the curve and observe how the y-coordinates change. The local maxima value of $y$ is $7$ , and this value occurs when $x$ is $0$ and the local minima value of $y$ is $-28.459$ , and this value occurs when $x$ is $1.709$ .

Interpretation:

From the above graph, it can be observed that there is only one local maximum and one local minima.The local maxima value of $y$ is $7$ , and this value occurs when $x$ is $0$ and the local minima value of $y$ is $-28.459$ , and this value occurs when $x$ is $1.709$ .