AP Calculus AB and BC - Analytical Applications of Differentiation

Dive into a comprehensive video review of Unit 5 in AP Calculus AB and BC, focusing on Analytical Applications of Differentiation. Learn key concepts such as the Mean Value Theorem, Extreme Value Theorem, critical points, and function behavior analysis. Master techniques for determining intervals of increase/decrease, finding local and global extrema, and analyzing concavity. Explore graph sketching, optimization problems, and implicit relations. Benefit from clear explanations, practical examples, and a structured approach to each topic, enhancing your understanding and preparation for AP exams. Access additional study resources, including summary videos, study guides, and practice questions, to further support your calculus learning journey.

- Introduction.
- 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.
- Summary.