Unit 5
AP Calculus AB Unit 5: Analytical Applications of Differentiation
The Mean Value Theorem and the Extreme Value Theorem, increasing and decreasing intervals, extrema, concavity, the first and second derivative tests, curve sketching, and optimization.
Topics
- 5.1Using the Mean Value Theorem
- 5.2Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- 5.3Determining Intervals on Which a Function Is Increasing or Decreasing
- 5.4Using the First Derivative Test to Determine Relative (Local) Extrema
- 5.5Using the Candidates Test to Determine Absolute (Global) Extrema
- 5.6Determining Concavity of Functions over Their Domains
- 5.7Using the Second Derivative Test to Determine Extrema
- 5.8Sketching Graphs of Functions and Their Derivatives
- 5.9Connecting a Function, Its First Derivative, and Its Second Derivative
- 5.10Introduction to Optimization Problems
- 5.11Solving Optimization Problems
- 5.12Exploring Behaviors of Implicit Relations
Unit check
12 questions drawn from every lesson in Unit 5. Each wrong answer links back to where the idea is taught.