Section 3.9 Worksheet:

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

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. Explain how implicit differentiation is involved in the subject of related rates. Give an example.

3. 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?

4. 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.