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Unit 5 of 10

Analytical Applications of Differentiation

This unit uses derivatives to analyze the shape and behavior of functions. Students study extrema, monotonicity, concavity, graph relationships, optimization, and implicit relations.

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UnitsLessons
  1. 02Differentiation: Definition and Basic Derivative Rules10
  2. 03Differentiation: Composite, Implicit, and Inverse Functions6
  3. 04Contextual Applications of Differentiation7
  4. 05Analytical Applications of Differentiation12
  5. 06Integration and Accumulation of Change14
  6. 07Differential Equations9
  7. 08Applications of Integration13
3 more units in the course outline
Units of AP® Calculus BC

Lessons

12 lessons in this unit

  1. 5.1Using the Mean Value TheoremPreview lesson
  2. 5.2Extreme Value Theorem, Global Versus Local Extrema, and Critical PointsPreview lesson
  3. 5.3Determining Intervals on Which a Function Is Increasing or DecreasingPreview lesson
  4. 5.4Using the First Derivative Test to Determine Relative (Local) ExtremaPreview lesson
  5. 5.5Using the Candidates Test to Determine Absolute (Global) ExtremaPreview lesson
  6. 5.6Determining Concavity of Functions over Their DomainsPreview lesson
  7. 5.7Using the Second Derivative Test to Determine ExtremaPreview lesson
  8. 5.8Sketching Graphs of Functions and Their DerivativesPreview lesson
  9. 5.9Connecting a Function, Its First Derivative, and Its Second DerivativePreview lesson
  10. 5.10Introduction to Optimization ProblemsPreview lesson
  11. 5.11Solving Optimization ProblemsPreview lesson
  12. 5.12Exploring Behaviors of Implicit RelationsPreview lesson

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