AP Unit 4: Contextual Applications of Differentiation
Find these readings by topic
This earlier reading list remains available with its complete tasks. The current book places these resources in the following topic chapters:
- Limits and continuity →
Connect approaching values across representations and justify continuity, asymptotes, and intermediate outputs.
- Derivatives as rates of change →
Explain and estimate an instantaneous rate, decide when it exists, and interpret its signed units.
- Differentiation tools →
Choose derivative rules for explicit, composite, inverse, and implicit functions while respecting domains.
- Graph shape and local approximation →
Use derivative evidence and theorem hypotheses to explain extrema, concavity, graphs, and nearby estimates.
- Modeling with derivatives →
Build motion, related-rate, and optimization models with meaningful variables, feasible domains, and justified conclusions.
Give derivatives a job: interpret changing quantities, connect motion, relate rates, estimate locally, and use L’Hospital’s Rule with its conditions.
Follow the topics below, then try the 30 unit problems before opening the separate step-by-step solutions.
- 4.1 Interpreting the Meaning of the Derivative in Context ↗
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration ↗
- 4.3 Rates of Change in Applied Contexts Other Than Motion ↗
- 4.4 Introduction to Related Rates ↗
- 4.5 Solving Related Rates Problems ↗
- 4.6 Approximating Values of a Function Using Local Linearity and Linearization ↗
- 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms ↗