Applications of the Derivative Chapter 3 Applications of the Derivative

Figure 3.1: Definition of Increasing and Decreasing Functions

Test for Increasing and Decreasing Functions

Figure 3.4: Definition of Critical Number

Guidelines for Applying Increasing/Decreasing Test

Figure 3.10: Definition of Relative Extrema

Figure 3.11: Occurrences of Relative Extrema

First-Derivative Test for Relative Extrema

Figure 3.12: First-Derivative Test

Definition of Absolute Extrema

Figure 3.16: Absolute Extrema

Extreme Value Theorem

Guidelines for Finding Extrema on a Closed Interval

Figure 3.20: Definition of Concavity

Test for Concavity

Guidelines for Applying Concavity Test

Figure 3.24: Definition of Point of Inflection

Property of Points of Inflection

Figure 3.26: Finding Points of Inflection

Figure 3.27: Second-Derivative Test

Guidelines for Solving Optimization Problems

Figure 3.41: Definition of Price Elasticity of Demand

Summary of Business Terms and Formulas

Figure 3.43: Graphs of the Demand, Revenue, Cost, and Profit Functions

Figure 3.44: Definition of Vertical Asymptote

Figure 3.49: Definition of Horizontal Asymptote

Horizontal Asymptotes of Rational Functions

Guidelines for Analyzing the Graph of a Function

Figure 3.60: Graphs of Polynomial Functions

Definition of Differentials

Figure 3.61: Tangent Line Approximation

Differential Forms of Differentiation Rules