Exercises for Lab #1

The following exercises are to be written-up and handed in on your own paper. You are encouraged to work in teams, but each team member should submit a separate lab report.

BE SURE TO INCLUDE THE FOLLOWING INFORMATION ON YOUR REPORT

Your name and the names of the people you worked with.
The name of your professor.
The day and time of your lab.

1. Open a new Maple worksheet and define a new function that maps x to -x^4-x^3+2*x^2 - 5 . Name your function f . Write the command you use on your lab report.

2. Use the Maple "plot" command to plot the graph of f on the closed interval [-2,0.5]. Sketch the resulting graph on your lab report. How many local maxima and minima does f appear to have on the interval?

3. Use Maple to compute the derivative of f . Write down the command you use.

4. As in the example, use Maple to find the maximum and minimum values of f on the interval [-2,0.5].

5. Use Maple's on-line help to learn how the "evalf" command can be used to evaluate an expression to a specified number of significant figures. Test your understanding by evaluating Pi to 20 significant figures. (Write the answer in your report.) Now compute the maximum and minimum values of f on the interval [-2,0.5] to twenty significant figures. Write the values in your lab report.