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SECTION 3.2 Basic Differentiation Rules and Rates of Change.

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Presentation on theme: "SECTION 3.2 Basic Differentiation Rules and Rates of Change."— Presentation transcript:

1 SECTION 3.2 Basic Differentiation Rules and Rates of Change

2 3.1 Additional Example 1

3 3.1 Additional Example 2a

4 3.1 Additional Example 2b

5 3.1 Additional Example 2c

6 Example 1 Theorem 3.2 The Constant Rule (p. 127)

7 More Differentiation Rules

8 Example 2

9 Example 3

10 Example 4 Derivative of the Natural Exponential Function

11 Example 5

12 Example 6

13 Example 7

14 Example 8

15 Physics Applications Average Velocity

16 Example 9

17 Position, Velocity & Accelaration Velocity Thus, “velocity is the derivative of position” “acceleration is the derivative of velocity.”

18 Example 10 Position Function of a Free-Falling Object (Neglecting Air-Resistance) A ball is thrown straight down from the top of a 220-ft building with an initial velocity of -22 ft per second. What is its velocity after 3 seconds? What is its velocity after falling 108 ft.?

19 Questions??? Don’t forget to be working the practice problems. Study hard!!! Test 1 on Tuesday!


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