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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

Let f(x)=x3−3x2+1f(x)=x^3-3x^2+1 on [−1,3].[-1,3]. Find and classify the absolute extrema of f.f.
Total: 5 points

(a) Explain why ff must have an absolute maximum and an absolute minimum on [−1,3][-1,3]. (1 point)

(b) Find all candidate xx-values for absolute extrema. (2 points)

(c) Determine the absolute maximum value and absolute minimum value. (2 points)

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