Unit 4 — contextual applications (Weeks 9–10)
- Related rates: cones, ladders, shadows, spheres — template: draw → relate → differentiate → substitute → units; implicit differentiation with respect to t
- Motion: position/velocity/acceleration; speed vs velocity; total distance = ∫|v|; particle-analysis FRQs (2011 AB #1a, 2015 3c acceleration)
- Linearization + tangent approximation; differentials; approximating with tangent line (2011 AB #5a)
- Unit 4 quiz + unit test + calculator motion FRQ (units required)
Unit 5 — analyzing functions (Weeks 11–12)
- EVT + MVT + Rolle: hypothesis checks + justification sentences (2015 AB 5c inflection, 2015 AB 6b vertical tangent)
- First derivative test, second derivative test, concavity + inflection; curve sketching with f/f'/f''; concavity reasoning (2017 AB/BC 4b)
- Optimization (fence, box, revenue); L'Hôpital review; Unit 5 quiz + unit test
- HALF-LENGTH AB DIAGNOSTIC + winter break: 20 mixed differentiation questions
Rubric drill: “f' changes + to − so f has local max” — no points without sign-change reference. CED: CHA-3–CHA-4, FUN-4.