Answer Key — Partial derivatives and optimization
Calculus III
Do not share with students before practice tests.
Worksheets — Sets 1–10
| Set | Guidance | | --- | --- | | Set 1 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 2 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 3 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 4 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 5 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 6 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 7 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 8 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 9 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 10 | Partial derivatives and optimization — verify written work and accept reasonable drawings. |
Worksheets — Sets 11–20
| Set | Guidance | | --- | --- | | Set 11 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 12 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 13 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 14 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 15 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 16 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 17 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 18 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 19 | Partial derivatives and optimization — verify written work and accept reasonable drawings. | | Set 20 | Partial derivatives and optimization — verify written work and accept reasonable drawings. |
Review tiers 1–10
- Checklists are parent-judged.
- Written items: verify against practice set patterns.
- Standard text: Functions of several variables; limits and continuity in R^n Partial derivatives, gradients, and directional derivatives Tangent planes, linearization, and the multivariable chain rule Lagrange multipliers and constrained optimization
Practice test scoring
| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |
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