1. AP CALCULUS AB Chapter 3: Derivatives Section 3.4: Velocity and Other Rates of Change

2. What you’ll learn about  Instantaneous Rates of change  Motion Along a Line  Sensitivity to Change  Derivatives in Economics … and why Derivatives give the rates at which things change in the world.

3. Instantaneous Rates of Change

4. Example Instantaneous Rates of Change

5. Ex: Find the rate of change of the Area of a square with respect to the length of a side when s = 4cm.

6. Motion Along a Line

7. Instantaneous Velocity

8. Speed

9. Acceleration

10. Free-fall Constants (Earth)

11. Section 3.4 – Velocity and Other Rates of Change  Position of an object (neglecting air resistance) under the influence of gravity, can be represented by where s 0 = original height of the object v 0 = original velocity of the object g = acceleration due to gravity

12. Example Finding Velocity

13. 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. This has applications in Biology and Physics.

14. Derivatives in Economics

15. Example Derivatives in Economics