Unit 5 Topics (College Board AP® Calculus AB): Revision Note

5.1

Using the Mean Value Theorem

• Mean Value Theorem

5.2

Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

• Extreme Value Theorem

• Critical Points

5.3

Determining Intervals on Which a Function Is Increasing or Decreasing

• Increasing & Decreasing Functions

5.4

Using the First Derivative Test to Determine Relative (Local) Extrema

• First Derivative Test for Local Extrema

5.5

Using the Candidates Test to Determine Absolute (Global) Extrema

• Candidates Test for Global Extrema

5.6

Determining Concavity of Functions over Their Domains

• Concavity of Functions

5.7

Using the Second Derivative Test to Determine Extrema

• Second Derivative Test for Local Extrema

5.8

Sketching Graphs of Functions and Their Derivatives

• Graphs of f, f' & f''

5.9

Connecting a Function, Its First Derivative, and Its Second Derivative

• Graphs of f, f' & f''

5.10

Introduction to Optimization Problems

• Optimization Problems

5.11

Solving Optimization Problems

• Optimization Problems

5.12

Exploring Behaviors of Implicit Relations

• Second Derivatives of Implicit Functions

• Critical Points of Implicit Relations