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 transcript:

Chapter 3 Applications of the Derivative

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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