### Chapter 3 - Palm Beach State College

```Chapter 3
Applications of
the Derivative
Figure 3.1: Definition of Increasing and
Decreasing Functions
3|2
Test for Increasing
and Decreasing Functions
3|3
Figure 3.4: Definition of
Critical Number
3|4
Guidelines for Applying
Increasing/Decreasing Test
3|5
Figure 3.10: Definition of
Relative Extrema
3|6
Figure 3.11: Occurrences of
Relative Extrema
3|7
First-Derivative Test
for Relative Extrema
3|8
Figure 3.12: First-Derivative Test
3|9
Definition of Absolute Extrema
3 | 10
Figure 3.16: Absolute Extrema
3 | 11
Extreme Value Theorem
3 | 12
Guidelines for Finding
Extrema on a Closed Interval
3 | 13
Figure 3.20: Definition of Concavity
3 | 14
Test for Concavity
3 | 15
Guidelines for
Applying Concavity Test
3 | 16
Figure 3.24: Definition of
Point of Inflection
3 | 17
Property of Points of Inflection
3 | 18
Figure 3.26: Finding Points
of Inflection
3 | 19
Figure 3.27: Second-Derivative Test
3 | 20
Guidelines for
Solving Optimization Problems
3 | 21
Figure 3.41: Definition of
Price Elasticity of Demand
3 | 22
Terms and Formulas
3 | 23
Figure 3.43: Graphs of the Demand,
Revenue, Cost, and Profit Functions
3 | 24
Figure 3.44: Definition of
Vertical Asymptote
3 | 25
Figure 3.49: Definition of
Horizontal Asymptote
3 | 26
Horizontal Asymptotes
of Rational Functions
3 | 27
Guidelines for Analyzing
the Graph of a Function
3 | 28
Figure 3.60: Graphs of
Polynomial Functions
3 | 29
Definition of Differentials