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