Chapter Four

Applications of Differentiation

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Definition of Extrema

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Definition of Relative Extrema

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Definition of a Critical Number

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Guidelines for Finding Extrema on a Closed Interval

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Rolle's Theorem

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The Mean Value Theorem

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Definitions of Increasing and Decreasing Functions

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Guidelines for Finding Intervals on Which a Function is Increasing or Decreasing

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The First Derivative Test

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Definition of Concavity

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Definition of Point of Inflection

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The Second Derivative Test

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Definition of Limits at Infinity

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Guidelines for Finding Limits at Infinity of Rational Functions

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Guidelines for Analyzing the Graph of a Function

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Guidelines for Solving Applied Minimum and Maximum Problems