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Applications of the Derivative
Chapter 3 Applications of the Derivative
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Figure 3.1: Definition of Increasing and Decreasing Functions
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Test for Increasing and Decreasing Functions
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Figure 3.4: Definition of Critical Number
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Guidelines for Applying Increasing/Decreasing Test
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Figure 3.10: Definition of Relative Extrema
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Figure 3.11: Occurrences of Relative Extrema
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First-Derivative Test for Relative Extrema
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Figure 3.12: First-Derivative Test
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Definition of Absolute Extrema
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Figure 3.16: Absolute Extrema
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Extreme Value Theorem
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Guidelines for Finding Extrema on a Closed Interval
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Figure 3.20: Definition of Concavity
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Test for Concavity
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Guidelines for Applying Concavity Test
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Figure 3.24: Definition of Point of Inflection
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Property of Points of Inflection
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Figure 3.26: Finding Points of Inflection
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Figure 3.27: Second-Derivative Test
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Guidelines for Solving Optimization Problems
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Figure 3.41: Definition of Price Elasticity of Demand
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Summary of Business Terms and Formulas
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Figure 3.43: Graphs of the Demand, Revenue, Cost, and Profit Functions
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Figure 3.44: Definition of Vertical Asymptote
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Figure 3.49: Definition of Horizontal Asymptote
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Horizontal Asymptotes of Rational Functions
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Guidelines for Analyzing the Graph of a Function
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Figure 3.60: Graphs of Polynomial Functions
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Definition of Differentials
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Figure 3.61: Tangent Line Approximation
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Differential Forms of Differentiation Rules
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