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 particle moves on the

x

-axis with velocity

v(t)=(5t-2)(t-4)

meters per second for

0\le t\le5.

Total: 6 points

(a) Find all times in $0\le t\le4$ when the particle is at rest. (1 point)

(b) Find the acceleration function $a(t)$ and the value of $a(2)$ . (1 point)

(c) Determine whether the particle moves left or right on each interval $(0,\frac25)$ , $(\frac25,4)$ , and $(4,5)$ . Justify your answer. (2 points)

(d) At $t=1$ , is the speed increasing, decreasing, or neither? Justify your answer. (2 points)

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

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