AP Unit 5: Analytical Applications of Differentiation
Find these readings by topic
This earlier reading list remains available with its complete tasks. The current book places these resources in the following topic chapters:
- Graph shape and local approximation →
Use derivative evidence and theorem hypotheses to explain extrema, concavity, graphs, and nearby estimates.
- Modeling with derivatives →
Build motion, related-rate, and optimization models with meaningful variables, feasible domains, and justified conclusions.
Use derivative evidence to justify what a function does: existence, extrema, monotonicity, concavity, graph connections, optimization, and implicit curves.
Follow the topics below, then try the 30 unit problems before opening the separate step-by-step solutions.
Course outline · Teacher guidance
This unit includes the shared AB core explicitly inside the BC book, with BC extensions where required. Each shared topic links to its AB source.
- 5.1 Using the Mean Value Theorem ↗
- 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points ↗
- 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing ↗
- 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema ↗
- 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema ↗
- 5.6 Determining Concavity of Functions over Their Domains ↗
- 5.7 Using the Second Derivative Test to Determine Extrema ↗
- 5.8 Sketching Graphs of Functions and Their Derivatives ↗
- 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative ↗
- 5.10 Introduction to Optimization Problems ↗
- 5.11 Solving Optimization Problems ↗
- 5.12 Exploring Behaviors of Implicit Relations ↗