Unit 5: Analytical Applications
Calculus AB · Unit 5 · Paper 1

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 1Paper 2Paper 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 1” 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
1

Concavity

2

Justifying an absolute extremum

3

Mean Value Theorem

4

Justification language

5

Reading f′ to describe f

6

Reading a graph of f′ to answer about f

7

First derivative test

8

Sketching f from f′

9

Second derivative test

10

Justifying an inflection point

11

Optimization justification

12

Critical point

Short answer 1. Define or explain: Comparing two functions on an interval

3 pts

Short answer 2. Define or explain: Point of inflection

3 pts

Short answer 3. Define or explain: Optimization procedure

3 pts

Short answer 4. Define or explain: Rolle's 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].