1. Bellwork

2. Quick Review

3. Bellwork Solutions

4. Quick Review Solutions

5. Velocity and Other Rates of Change
Chapter 3
Derivatives
Section 3.4
Velocity and Other Rates of Change

6. What you’ll learn about
Instantaneous rates of change
Motion on a line
Acceleration as the second derivative
Modeling vertical motion and particle motion
The derivative as a measure of sensitivity to change
Marginal cost and marginal revenue
… and why
Derivatives give the rates at which things change
in the world.

7. Instantaneous Rates of Change

8. Example Instantaneous Rates of Change

9. You Try

10. The rate of change in area of a circle get's larger as it's radius get's larger.

11. Motion Along a Line

13. Instantaneous Velocity

14. Speed

16. Acceleration

17. Free-fall Constants (Earth)

18. Example Finding Velocity

23. You Try

26. Sensitivity to Change
When a small change in x produces a large change in the value of a function f (x), we say that the function is relatively sensitive to changes in x. The derivative f ′ (x) is a measure of this sensitivity.

28. Derivatives in Economics

30. Example Derivatives in Economics

32. Homework