Chapter 3
Applications of
Differentiation
Definition of Extrema
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Figure 3.1
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Theorem 3.1 The Extreme Value Theorem
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Definition of Relative Extrema
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Figure 3.2
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Definition of a Critical Number and Figure 3.4
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Theorem 3.2 Relative Extrema Occur Only at
Critical Numbers
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Guidelines for Finding Extrema on a Closed
Interval
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Theorem 3.3 Rolle's Theorem and Figure 3.8
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Theorem 3.4 The Mean Value Theorem and
Figure 3.12
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Definitions of Increasing and Decreasing
Functions and Figure 3.15
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Theorem 3.5 Test for Increasing and
Decreasing Functions
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Guidelines for Finding Intervals on Which a
Function Is Increasing or Decreasing
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Theorem 3.6 The First Derivative Test
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Definition of Concavity and Figure 3.24
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Theorem 3.7 Test for Concavity
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Definition of Point of Inflection and
Figure 3.28
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Theorem 3.8 Points of Inflection
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Theorem 3.9 Second Derivative Test and
Figure 3.31
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Definition of Limits at Infinity and Figure 3.34
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Definition of a Horizontal Asymptote
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Theorem 3.10 Limits at Infinity
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Guidelines for Finding Limits at +/- infinity of
Rational Functions
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Definition of Infinite Limits at Infinity
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Guidelines for Analyzing the Graph of a
Function
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Figure 3.54
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Guidelines for Solving Applied Minimum and
Maximum Problems
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Newton's Method for Approximating the
Zeroes of a Function
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Definition of Differentials
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Differential Formulas
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