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Chapter 2 Differentiation. Copyright © Houghton Mifflin Company. All rights reserved.2 | 2 Tangent Line to a Graph.

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Presentation on theme: "Chapter 2 Differentiation. Copyright © Houghton Mifflin Company. All rights reserved.2 | 2 Tangent Line to a Graph."— Presentation transcript:

1 Chapter 2 Differentiation

2 Copyright © Houghton Mifflin Company. All rights reserved.2 | 2 Tangent Line to a Graph

3 Copyright © Houghton Mifflin Company. All rights reserved.2 | 3 Tangent Line to a Circle

4 Copyright © Houghton Mifflin Company. All rights reserved.2 | 4 Tangent Line to a Graph at a Point

5 Copyright © Houghton Mifflin Company. All rights reserved.2 | 5 The Secant Line Through the Two Points

6 Copyright © Houghton Mifflin Company. All rights reserved.2 | 6 Secant line approaches the tangent line

7 Copyright © Houghton Mifflin Company. All rights reserved.2 | 7 Definition of the Slope of a Graph

8 Copyright © Houghton Mifflin Company. All rights reserved.2 | 8

9 Copyright © Houghton Mifflin Company. All rights reserved.2 | 9 Definition of the Derivative

10 Copyright © Houghton Mifflin Company. All rights reserved.2 | 10 Functions That Are Not Differentiable at x = 0

11 Copyright © Houghton Mifflin Company. All rights reserved.2 | 11

12 Copyright © Houghton Mifflin Company. All rights reserved.2 | 12 The Constant Rule

13 Copyright © Houghton Mifflin Company. All rights reserved.2 | 13 The (Simple) Power Rule

14 Copyright © Houghton Mifflin Company. All rights reserved.2 | 14 The Constant Multiple Rule

15 Copyright © Houghton Mifflin Company. All rights reserved.2 | 15 The Sum and Difference Rules

16 Copyright © Houghton Mifflin Company. All rights reserved.2 | 16 Definition of Average Rate of Change

17 Copyright © Houghton Mifflin Company. All rights reserved.2 | 17 Definition of Instantaneous Rate of Change

18 Copyright © Houghton Mifflin Company. All rights reserved.2 | 18

19 Copyright © Houghton Mifflin Company. All rights reserved.2 | 19 The Product Rule

20 Copyright © Houghton Mifflin Company. All rights reserved.2 | 20

21 Copyright © Houghton Mifflin Company. All rights reserved.2 | 21 The Quotient Rule

22 Copyright © Houghton Mifflin Company. All rights reserved.2 | 22

23 Copyright © Houghton Mifflin Company. All rights reserved.2 | 23

24 Copyright © Houghton Mifflin Company. All rights reserved.2 | 24 The Chain Rule

25 Copyright © Houghton Mifflin Company. All rights reserved.2 | 25

26 Copyright © Houghton Mifflin Company. All rights reserved.2 | 26 The General Power Rule

27 Copyright © Houghton Mifflin Company. All rights reserved.2 | 27 Summary of Differentiation Rule

28 Copyright © Houghton Mifflin Company. All rights reserved.2 | 28 Marginal Profit/Marginal Revenue/Marginal Cost

29 Copyright © Houghton Mifflin Company. All rights reserved.2 | 29

30 Copyright © Houghton Mifflin Company. All rights reserved.2 | 30

31 Copyright © Houghton Mifflin Company. All rights reserved.2 | 31 Notation for Higher-Order Derivatives

32 Copyright © Houghton Mifflin Company. All rights reserved.2 | 32

33 Copyright © Houghton Mifflin Company. All rights reserved.2 | 33 Position Function/Velocity Function/Acceleration Function

34 Copyright © Houghton Mifflin Company. All rights reserved.2 | 34

35 Copyright © Houghton Mifflin Company. All rights reserved.2 | 35 Implicit Differentiation

36 Copyright © Houghton Mifflin Company. All rights reserved.2 | 36 Table: Verbal Statement/ Mathematical Model

37 Copyright © Houghton Mifflin Company. All rights reserved.2 | 37 Guidelines for Solving a Related-Rate Problem

38 Copyright © Houghton Mifflin Company. All rights reserved.2 | 38

39 Copyright © Houghton Mifflin Company. All rights reserved.2 | 39

40 Copyright © Houghton Mifflin Company. All rights reserved.2 | 40

41 Copyright © Houghton Mifflin Company. All rights reserved.2 | 41

42 Copyright © Houghton Mifflin Company. All rights reserved.2 | 42

43 Copyright © Houghton Mifflin Company. All rights reserved.2 | 43

44 Copyright © Houghton Mifflin Company. All rights reserved.2 | 44

45 Copyright © Houghton Mifflin Company. All rights reserved.2 | 45

46 Copyright © Houghton Mifflin Company. All rights reserved.2 | 46

47 Copyright © Houghton Mifflin Company. All rights reserved.2 | 47

48 Copyright © Houghton Mifflin Company. All rights reserved.2 | 48

49 Copyright © Houghton Mifflin Company. All rights reserved.2 | 49

50 Copyright © Houghton Mifflin Company. All rights reserved.2 | 50

51 Copyright © Houghton Mifflin Company. All rights reserved.2 | 51

52 Copyright © Houghton Mifflin Company. All rights reserved.2 | 52

53 Copyright © Houghton Mifflin Company. All rights reserved.2 | 53 Find the slope of the graph at the given point.


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