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Marlow Works

AP Calculus AB / Unit 4

Unit 4 · 10–15%

Contextual Applications of Differentiation

Rates in the world come in pairs: if one quantity moves, a related one often does too.

Start first lessonUnit practice

Topics

  • Interpreting derivatives in context
  • Related rates
  • Linearization
  • L’Hospital’s rule for 0/0 and ∞/∞ forms

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. 01Assign variables and units before differentiating a related-rates story.
  2. 02State which quantities are changing with time and which are constant.
  3. 03Write the interpretive sentence with the word instantaneous or at that instant.

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