Calculus AB · Unit 5 · Paper 3

Analytical Applications unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 17 terms and is the same for everyone, so a teacher can assign “Unit 5, Paper 3” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 36 min 33 points0/17 attempted

Reading a graph of f′ to answer about f

Justification language

Sketching f from f′

First derivative test

Concavity

Candidates test for absolute extrema

Critical point

Justifying an absolute extremum

Point of inflection

Optimization procedure

Comparing two functions on an interval

Second derivative test

Short answer 1. Define or explain: Rolle's Theorem

3 pts

Short answer 2. Define or explain: Justifying an inflection point

3 pts

Short answer 3. Define or explain: Optimization justification

3 pts

Short answer 4. Define or explain: Mean Value Theorem

3 pts

Free response

9 pts

Let f(x) = x³ − 6x² + 9x + 2.

Find all critical points of f and classify each as a local maximum or local minimum. Justify your answer.

Find the inflection point of f and the interval on which f is concave up.

Find the absolute maximum and absolute minimum values of f on the closed interval [0, 4].