Review
Chapter 2 and 4.1-4.4
MA 160

For Spring '99:
Test #2 covers ONLY chapter 2, so ignore points 15-19 below.

1. What is a derivative? (give at least two answers)
2. How can you approximate the derivative at a point from a graph?
3. How can you approximate the derivative at a point from a function given by a formula?
4. How can you approximate the derivative at a point from a table of function values?
5. Give a graph of a function f(x), how can you sketch a graph of the derivative function f'(x)?
6. What is the difference between ``average velocity'' and ``instantaneous velocity''? How do you compute each, given position s as a function of time t?
7. Suppose a function f is measured in flugels and it is a function of x, measured in xiapets. What are the units of ?
8. What is the limit definition of derivative? How is it related to an average rate of change? Why does it involve a limit?
9. Explain why the following two statements are NOT saying the same thing: (1) ``f is increasing'' vs. (2) ``the slope of f is increasing''. What do each of these statements mean?
10. Given a graph of a function f and a point on the graph x, what do the following quantities represent: f(x)? f(x+h)? f(x+h)-f(x)? h? What do these all have to do with derivatives?
11. If a function f(x) is increasing, what does that say about f'(x)? Does it say anything about f''(x)?
12. Suppose we know that f'(x) (the derivative of a function f) is positive and increasing. What does that say about the graph of f'(x)? What about f''(x)?
13. What does the second derivative, f''(x) tell you about the graph of f(x)?
14. Explain why acceleration is the second derivative of the position function.
15. Given a formula for a function f(x), how do you find the equation for the line tangent to f at x=3?
16. For which kinds of functions do we have formulas for the derivative?
17. How can you tell the difference between a power function and an exponential function? What are the derivative formulas in each case?
18. What are the product and quotient rules? How do you know if you need to use them?
19. What is the chain rule and why do we need it?

Besides thinking about the questions above, here are some other ways to study for the test:

• Skim through each section of the book and write down a few words about what the BIG IDEA in that section.
• Practice using the formula for derivatives (Ch.4) by generating a random quiz (see my web page).
• Re-read your worksheets, and remind yourself what was the point of each new idea.
• Look at the scoop on reserve in the library.
• Review your quizzes on this material.
• Review your homework on this material.
• Read through the examples in the book, and after going through each try to summarize the procedure or idea in a few sentences.
• Memorize formulas that you will need.
• Read through the review problems in the book and decide how you would approach each one.