Calc AB · U4
Contextual Applications of Differentiation
Use derivatives to interpret real situations, solve motion and related-rates problems, approximate values, and evaluate indeterminate limits with L'Hospital's Rule.
Test yourself
A focused, distraction-free run through 35 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 4.1
Interpreting the Meaning of the Derivative in Context
Reading derivative values, signs, and units as rates of change in real situations
Topic 4.2
Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Using derivatives to connect position, velocity, acceleration, direction, rest, and speed behavior
Topic 4.3
Rates of Change in Applied Contexts Other Than Motion
Applying derivative relationships in area, volume, cost, revenue, temperature, and population contexts
Topic 4.4
Introduction to Related Rates
Choosing variables and differentiating geometric relationships with respect to time
Topic 4.5
Solving Related Rates Problems
Completing multi-step related rates problems in geometric and applied contexts
Topic 4.6
Approximating Values of a Function Using Local Linearity and Linearization
Using tangent lines and differentials to approximate values and reason about overestimates or underestimates
Topic 4.7
Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
Applying L'Hospital's Rule with justification, including repeated use and non-applicable forms