FRQ — Contextual Applications of Differentiation

Free response·Hard exam skill (4/5)·No calculatorNeeds mentor review

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.

Question

A circular stain has radius

r(t)

centimeters at time

t

minutes. At

t=10,\ r=6

and

\frac{dr}{dt}=0.4.

Total: 6 points

(a) Find the rate at which the area of the stain is changing at $t=10$ . (2 points)

(b) Suppose also that $\frac{d^2r}{dt^2}=-0.03$ at $t=10$ . Find $\frac{d^2A}{dt^2}$ at $t=10$ . (3 points)

Your response (optional — you can also work on paper)

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