Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 2.1

1. The second paragraph on page 93 gives the basic idea behind derivatives. What is it?
2. After you finish reading through the end of page 94, try to rewrite this basic idea in your own words-what are your first impressions of what it means to you?
3. Write down the definition of the derivative as rate function.
4. Take a closer look at the graph of P(t) on page 95. Between time t = 0 and t = 3, the graph rises-this means the car is moving farther east from Bismarck. What does it mean when the graph falls?
5. At time t = 3, the graph of P(t) switches from rising to falling. What is the value V(3)? Does this make physical sense? Explain.
6. Explain the graphical relationship between the two graphs on page 95.
7. What is the definition of slope?
8. What is the definition of the derivative as a slope function?
9. Explain in your own words what the tangent line at a point is. You may want to use the picture on page 99 to help describe it.
10. How are the two descriptions of derivative-rate function and slope function-related?
11. In your own words, explain the racetrack principle and its relation to functions.
12. On page 103, what do the constants h₀ and v₀ represent in the formulas? Where do the 6 and 100 come from in the example?
13. The example claims that "Height is greatest at the instant when upward velocity is zero." Why??
14. How is this represented in the graphs on page 103?
15. When the height of the ball is increasing, describe graphically what the velocity function is doing. Do the same for when the height of the ball is decreasing.
16. What is a differential equation?
17. What is a solution to a differential equation?