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Marlow Works

AP Calculus AB / Unit 5

Unit 5 · 15–20%

Analytical Applications of Differentiation

Derivatives find peaks, justify mean-value claims, and set up optimization.

Start first lessonUnit practice

Topics

  • Mean Value Theorem
  • First and second derivative tests
  • Concavity and inflection
  • Optimization

Lessons

Key terms

Original practice

Marlow Works questions. If this unit does not have its own items yet, you will see other questions from the same course.

1 of 3Limits and Continuity · easy · multiple choice

What is lim (x→3) of (x² − 9) / (x − 3)?

Original Marlow Works item — not a College Board question.

Take your time—this is practice, not a test.

Review checklist

  1. 01State the hypotheses of a theorem before you invoke the conclusion.
  2. 02Make a sign chart that matches the domain.
  3. 03In a worded optimum, say what the maximum is and where it occurs.

Related resources

External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.

  • Official / link only

    AP Calculus AB course page

    Official eight-unit framework and 2027 exam updates.

    College Board · All rights reserved · accessed 2026-10-01

    Open source

  • Reference only — do not copy

    OpenStax College Algebra 2e

    Algebra reference; current terms include noncommercial and AI-ingestion limits.

    OpenStax · Restricted — see publisher page · accessed 2026-10-01

    Open source