Lesson 3.1 · AP 4.1–4.5
Motion, units, and related rates
Translate changing quantities into derivative equations, distinguish speed from velocity, and preserve units.
Reading reference: Larson & Edwards §§2.6, 3.9
Read lesson →← Calculus Honors Study Guide
Unit 3
Applications of Differentiation
Where the rules become arguments. Extremes, shape, optimization, and related rates all ask the student to justify a conclusion from derivative evidence.
Unit 3 practice
15 problems · Questions and worked solutions.
Lessons
Lesson 3.2 · AP 5.1–5.5
Critical points, extrema, and the Mean Value Theorem
Separate candidates from conclusions, compare endpoint values, and verify hypotheses before invoking a theorem.
Reading reference: Larson & Edwards §§3.1–3.3
Read lesson →Lesson 3.3 · AP 5.3–5.9
Derivative graphs, concavity, and curve analysis
Read a function’s behavior from first- and second-derivative evidence rather than from the height of a derivative graph.
Reading reference: Larson & Edwards §§3.3–3.4, 3.6
Read lesson →Lesson 3.4 · AP 5.10–5.11
Optimization: constraints, domains, and justification
Turn a geometric or contextual goal into a one-variable function, then prove the candidate gives the requested optimum.
Reading reference: Larson & Edwards §3.7
Read lesson →Lesson 3.5 · AP 4.6–4.7
Linear approximation and L’Hôpital’s Rule
Use tangent lines for local estimates, distinguish approximation error from concavity, and resolve eligible indeterminate limits.
Reading reference: Larson & Edwards §3.9; §8.7
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