Section 3.1 Worksheet:

Assigned problems: Exercises pp. 134-135, #1, 2, 6, 8, 16, 20, 25, 32 (due Wednesday)

1. The author offers two different ``interpretations'' of the derivative. What are they?

2. In this section we speak of the derivative of f at a point (x=2, say). What conditions must exist in order for the derivative of f to exist at x=2?

3. Explain why calculating the derivative of f at an unspecified point x=a (of the domain of f) gives rise to a function on a subset of the domain.

4. Why do the units of a derivative always turn out to be ``something per something else''? (Give some examples!)

5. When does it make sense to talk about derivatives in the case of tabular data (e.g. Example 6, p. 133)? When not?

Notes:

1. I've told you to keep your eye on the slope. Another buzz word in this section (and for the course) is ``change''. The derivative is an instrument that measures change in a function, which is reflected in the steepness of the graph.