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Library AP Calculus AB/BC Unit 5: Analytical Applications of Differentiation
⁂   AP Calculus AB/BC · Unit 5

5. Analytical Applications of Differentiation

15–18% of the AP exam. Key topics: Mean Value Theorem (MVT), Extreme Value Theorem (EVT), Critical points and local extrema, First derivative test for local maxima and minima, Second derivative test for local maxima and minima, Concavity and inflection points, Global (absolute) extrema on closed intervals, Optimization problems, Curve sketching using derivatives.

15 instructional periods 15–18% exam weight AB track

Unit 5: Analytical Applications of Differentiation

Study guide content for this unit is being prepared. Check back soon for complete lesson notes, formula sheets, and worked examples.

Topics in this unit

  • Mean Value Theorem (MVT)
  • Extreme Value Theorem (EVT)
  • Critical points and local extrema
  • First derivative test for local maxima and minima
  • Second derivative test for local maxima and minima
  • Concavity and inflection points
  • Global (absolute) extrema on closed intervals
  • Optimization problems
  • Curve sketching using derivatives

Worked FRQ Solutions

Free-response questions from past AP exams that test this unit's concepts.