Lesson #77
Applied Maximum Minimum Problems -- Mini Golf




Quote of the Day:
"Starting in the seventeenth century, the general theory of extreme values -- maxima and minima -- has become one of the systematic integrating principles of science."
-- Richard Courant and Herbert Robbins

Objectives:
The student will learn to solve applied maximum minimum problems.



1. Collect Homework.

2. Distribute Rulers, Protractors, and Mini golf worksheets.

Have students experiment to find the point that yields the minimum distance - this is also the point at which the ball would rebound and go in the hole.

Show geometric proof. Have students set up the calculus proof.

Worksheet on Billiards and Mini Golf

3. Example:
Problem #2-2 from the December 3, 1991 Virginia Math League Contest

Given: The sum of the lengths of the 2 legs of a right triangle is 20 inches. What is the smallest possible length of the hypotenuse of this triangle?

Solution:
Let x = length of one leg.
Then 20 - x = the length of other leg.
Let c = length of hypotenuse.


4. Video on Billiards (ESPN)



5. Assignment:
Worksheet on Billiards and Mini Golf
Design your own Mini Golf hole on Graph Paper
p. 318 (1, 3, 5, 24, 25)
Worksheet on the Longest Home Run

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Send any comments or questions to: David Pleacher