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Chapter 3 Applications of the Derivative. Copyright © Houghton Mifflin Company. All rights reserved.3 | 2 Figure 3.1: Definition of Increasing and Decreasing.

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Presentation on theme: "Chapter 3 Applications of the Derivative. Copyright © Houghton Mifflin Company. All rights reserved.3 | 2 Figure 3.1: Definition of Increasing and Decreasing."— Presentation transcript:

1 Chapter 3 Applications of the Derivative

2 Copyright © Houghton Mifflin Company. All rights reserved.3 | 2 Figure 3.1: Definition of Increasing and Decreasing Functions

3 Copyright © Houghton Mifflin Company. All rights reserved.3 | 3 Test for Increasing and Decreasing Functions

4 Copyright © Houghton Mifflin Company. All rights reserved.3 | 4 Figure 3.4: Definition of Critical Number

5 Copyright © Houghton Mifflin Company. All rights reserved.3 | 5 Guidelines for Applying Increasing/Decreasing Test

6 Copyright © Houghton Mifflin Company. All rights reserved.3 | 6 Figure 3.10: Definition of Relative Extrema

7 Copyright © Houghton Mifflin Company. All rights reserved.3 | 7 Figure 3.11: Occurrences of Relative Extrema

8 Copyright © Houghton Mifflin Company. All rights reserved.3 | 8 First-Derivative Test for Relative Extrema

9 Copyright © Houghton Mifflin Company. All rights reserved.3 | 9 Figure 3.12: First-Derivative Test

10 Copyright © Houghton Mifflin Company. All rights reserved.3 | 10

11 Copyright © Houghton Mifflin Company. All rights reserved.3 | 11

12 Copyright © Houghton Mifflin Company. All rights reserved.3 | 12

13 Copyright © Houghton Mifflin Company. All rights reserved.3 | 13

14 Copyright © Houghton Mifflin Company. All rights reserved.3 | 14 Definition of Absolute Extrema

15 Copyright © Houghton Mifflin Company. All rights reserved.3 | 15 Figure 3.16: Absolute Extrema

16 Copyright © Houghton Mifflin Company. All rights reserved.3 | 16 Extreme Value Theorem

17 Copyright © Houghton Mifflin Company. All rights reserved.3 | 17 Guidelines for Finding Extrema on a Closed Interval

18 Copyright © Houghton Mifflin Company. All rights reserved.3 | 18

19 Copyright © Houghton Mifflin Company. All rights reserved.3 | 19

20 Copyright © Houghton Mifflin Company. All rights reserved.3 | 20

21 Copyright © Houghton Mifflin Company. All rights reserved.3 | 21 Figure 3.20: Definition of Concavity

22 Copyright © Houghton Mifflin Company. All rights reserved.3 | 22 Test for Concavity

23 Copyright © Houghton Mifflin Company. All rights reserved.3 | 23 Guidelines for Applying Concavity Test

24 Copyright © Houghton Mifflin Company. All rights reserved.3 | 24 Figure 3.24: Definition of Point of Inflection

25 Copyright © Houghton Mifflin Company. All rights reserved.3 | 25 Property of Points of Inflection

26 Copyright © Houghton Mifflin Company. All rights reserved.3 | 26 Figure 3.26: Finding Points of Inflection

27 Copyright © Houghton Mifflin Company. All rights reserved.3 | 27 Figure 3.27: Second-Derivative Test

28 Copyright © Houghton Mifflin Company. All rights reserved.3 | 28

29 Copyright © Houghton Mifflin Company. All rights reserved.3 | 29

30 Copyright © Houghton Mifflin Company. All rights reserved.3 | 30 Guidelines for Solving Optimization Problems

31 Copyright © Houghton Mifflin Company. All rights reserved.3 | 31 Figure 3.41: Definition of Price Elasticity of Demand

32 Copyright © Houghton Mifflin Company. All rights reserved.3 | 32 Summary of Business Terms and Formulas

33 Copyright © Houghton Mifflin Company. All rights reserved.3 | 33 Figure 3.43: Graphs of the Demand, Revenue, Cost, and Profit Functions

34 Copyright © Houghton Mifflin Company. All rights reserved.3 | 34

35 Copyright © Houghton Mifflin Company. All rights reserved.3 | 35

36 Copyright © Houghton Mifflin Company. All rights reserved.3 | 36

37 Copyright © Houghton Mifflin Company. All rights reserved.3 | 37

38 Copyright © Houghton Mifflin Company. All rights reserved.3 | 38 Figure 3.44: Definition of Vertical Asymptote

39 Copyright © Houghton Mifflin Company. All rights reserved.3 | 39 Figure 3.49: Definition of Horizontal Asymptote

40 Copyright © Houghton Mifflin Company. All rights reserved.3 | 40 Horizontal Asymptotes of Rational Functions

41 Copyright © Houghton Mifflin Company. All rights reserved.3 | 41 Guidelines for Analyzing the Graph of a Function

42 Copyright © Houghton Mifflin Company. All rights reserved.3 | 42 Figure 3.60: Graphs of Polynomial Functions

43 Copyright © Houghton Mifflin Company. All rights reserved.3 | 43 Definition of Differentials

44 Copyright © Houghton Mifflin Company. All rights reserved.3 | 44 Figure 3.61: Tangent Line Approximation

45 Copyright © Houghton Mifflin Company. All rights reserved.3 | 45

46 Copyright © Houghton Mifflin Company. All rights reserved.3 | 46

47 Copyright © Houghton Mifflin Company. All rights reserved.3 | 47

48 Copyright © Houghton Mifflin Company. All rights reserved.3 | 48

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