Chapter 3.2, Problem 64E

To determine

To graph and compare the each function.

Explanation of Solution

Given information: the functionis $y=1.2x^5+3.75x^4-7x^3-15x^2+18$ .

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 $\text{Y=}1.2x^5+3.75x^4-7x^3-15x^2+18$ which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

There appears to be two local maxima,first local maxima is occurring at $x=-3$ and the second local maxima is in between $x=0$ and $x=1$ and there are also two local minima one local minima is between $x=-1$ and $x=-2$ and the second local minima is between $x=1$ 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 first local maxima value of $y$ is $12.15$ , and this value occurs when $x$ is $-3$ and second local maxima value of $y$ is $4.647$ , and this value occurs when $x$ is $0.5$ , the first local minima value of $y$ is $-27.445$ and this occurs when $x$ is $-1.414$ and the second local minima value of $y$ is $4.467$ and this value occurs when $x$ is $0.5$ .

Interpretation:

From the above graph, it can be observed that there is two local maxima and two local minima. The first local maxima value of $y$ is $12.15$ , and this value occurs when $x$ is $-3$ and second local maxima value of $y$ is $4.647$ , and this value occurs when $x$ is $0.5$ , the first local minima value of $y$ is $-27.445$ and this occurs when $x$ is $-1.414$ and the second local minima value of $y$ is $4.467$ and this value occurs when $x$ is $0.5$ .