Activity 1. Here are some examples illustrating the use of the Extreme Value Theorem to find the absolute maximum and minimum values of continuous functions on closed intervals. Recall that the theorem states that the absolute max and min will occur at either an end point or at a critical value. You can use the buttons on the web page to see graphs of the functions and also completely worked solutions (they show how to find and check the critical values). You can ignore the third, seventh, and tenth problems as they contain trigonometric functions. The other seven are good examples of what you might see in Math 175.
|
Activity 2. Here are 21 examples of applied max/min problems with detailed solutions. Some of the problems are a bit more difficult than the ones we are discussing in Math 175, but they are all interesting. Problems 1, 2, 3, 4, 5, 8, 9, 10, and 11 are at the level of the problems in our textbook (so try them first). Try to work through these examples and refer to the detailed solutions only when you get stuck. Find a solution to this problem: A closed rectangular box (4 sides, a top and a bottom) with a square base is to be made from 600 square inches of material. What dimensions will result in a box with the largest possible volume? Hint: Match this question to one of the examples mentioned above. Solve the problem and email your instructor the function that you build and the answer to the question. If your email program is configured properly, you can click on one of the names below. Use the subject line `Your Name, Math 175 Applied Max/Min'. |
|