FRQ — Integration and Accumulation of Change

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

The figure shows aligned graphs of

A, f,

and

f'

0\le x\le6.

They satisfy

A'(x)=f(x)

and

A''(x)=f'(x),

with

A(0)=2.

Total: 6 points

(a) Use signed area from the graph of $f$ to find $A(2)$ and $A(4)$ . (2 points)

(b) Find the $x$ -coordinates of all local extrema of $A$ on $(0,6)$ and classify each. Justify your answer. (2 points)

(c) Determine where $A$ is concave up, where $A$ is linear, and where $A$ is concave down. Justify using the graph of $f'$ . (2 points)

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

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