Maple Lab Week 17

Applied Max/Min Problems

Objectives: In this lab you will use Maple to work some applied max/min problems that lead to algebraic calculations that are rather difficult to do by hand. The thinking needed to convert the ``word problems'' into mathematical equations and functions will still be your responsibility. This exercise demonstrates both the power and limitations of computer algebra.

Before the lab: Write out solutions to the following three problems, and hand them in at the beginning of the lab period. These exercises are to be done by hand. Note that the first two are also assigned homework problems. You are encouraged to look ahead at the last three problems below, which are to be solved during the lab period, so that you will already know how to ``set them up''.

• Stewart Sect. 3.8, Problem 10
• Stewart Sect. 3.8, Problem 13
• CalcLabs Chapter 6, Problem 4

Lab Exercises: Write out solutions using Maple to the following exercises from CalcLabs Chapter 6. Include both an analytical solution and a graphical solution, i.e., using a graph of the quantity to be optimized vs. some independent variable, and the coordinates of the point (obtained by clicking on the point with your mouse) corresponding to the optimum solution.

• Problem 1 (volume of a box).
• Problem 2 (distance to a curve).
• Problem 5 (viewing angle of a movie screen).