Free response·Challenge (5/5)·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
Squares of side are cut from each corner of a by sheet, and the sides are folded up to form an open-top box.
Total: 6 points
(a) Write the volume and state its domain. (2 points)
(b) Find the value of that maximizes the volume. (3 points)
(c) Justify that your value gives an absolute maximum. (1 point)
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