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AP Calculus AB
Unit 1: Limits and Continuity
Unit 2: Differentiation: Definition and Fundamental Properties
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
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
Unit 6: Integration and Accumulation of Change
Unit 7: Differential Equations
Unit 8: Applications of Integration
AP/Calculus AB/Concept/Unit 5: Analytical Applications of Differentiation

Unit 5: Analytical Applications of Differentiation

Syllabus
2020
Section
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Level
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Exam analysis

Most tested topics

  1. Using the Mean Value Theorem
  2. Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
  3. Determining Intervals on Which a Function Is Increasing or Decreasing
  4. Using the First Derivative Test to Determine Relative (Local) Extrema
  5. Using the Candidates Test to Determine Absolute (Global) Extrema
  6. Determining Concavity of Functions over Their Domains
  7. Using the Second Derivative Test to Determine Extrema
  8. Sketching Graphs of Functions and Their Derivatives
  9. Connecting a Function, Its First Derivative, and Its Second Derivative
  10. Introduction to Optimization Problems
  11. Solving Optimization Problems
  12. Exploring Behaviors of Implicit Relations