Chapter 3.2, Problem 54E

To determine

To graph and compare the each function.

Explanation of Solution

Given information: the functionis $y=2x^3-3x^2-12x-32$ .

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 $\text{Y=}2x^3-3x^2-12x-32$ 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 at $x=-1$ and one minima at $x=2$ . 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 $-25$ , and this value occurs when $x$ is $-2$ and the local minima value of $y$ is $-52$ , and this value occurs when $x$ is $2$ .

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 $-25$ , and this value occurs when $x$ is $-2$ and the local minima value of $y$ is $-52$ , and this value occurs when $x$ is $2$ .