Section 4.10 Worksheet:

Assigned problems: Exercises pp. 304-306, #4, 9, 28, 32, 41, 56, 65, 69 (due Friday, 3/21).

1. What is the relationship between the concept of derivative and the concept of anti-derivative? Do the two functions vaporize when they collide?

2. What do the members of the family of functions in Figure 1, p. 299, have in common?

3. Add three more entries to the table on page 300.

4. Describe in your own words the direction field.

5. What is a differential equation? Give an example.

Notes:

• This chapter has us ``thinking backwards'', and this is a skill which takes times and practice to master. Whereas differentiation is essentially a mechanical exercise, anti-differentiation may require insight, and broad exposure to lots of different functions. One asks oneself, ``do I know a function whose derivative looks like this?''
• Starting from the derivative(s), and perhaps initial conditions (e.g. the value of the function at a point), we may be able to use direction fields to trace a pretty good representation of the function, and then deduce a formula from that.