Section 3.9 Worksheet:

Assigned problems: Exercises pp. 203-205, #5-8, 18, 22, 25, 28, 32 (due Friday, 2/21).

1. The name itself, related rates, indicates that we will be required to relate two (or more!) rates (i.e. derivatives). What is the strategy for solving these problems as suggested by the book?

2. There is Warning in this section. What is it? Can you give a different example that illustrates the problem?

3. Principles of Problem Solving are mentioned in this section. What are the four steps listed?

4. In example 2 (the ladder problem, which is a very famous problem indeed), what fundamental equation (or equations) allows us to solve this problem of relating the rate of slide to the rate of drop?

5. In example 3 (the inverted water tank), what is the fundamental equation (or equations) which allows us to solve this problem of relating the rate of the rise of water to the rate of increase of volume?

Notes:

1. This section challenges you to use every mathematical relationship you know (e.g. the Pythagorean Theorem, definitions of trig functions, area and volume formulas, etc.). Many of the problems are given in the form of the dreaded word problem, which you are rapidly learning to love.
2. Number one rule of story problems, or word problems: Draw a picture! You will be amazed at how it will help you to solve problems if you will only draw pictures, and label them carefully, and then establish the proper mathematical relationships between the variables.