← MATH 01130 · Calculus I
MATH 01130 · Applications of derivatives
Optimization word problems
Definition
Maximize/minimize a quantity subject to a constraint. Express objective as a single-variable function, find critical points on a realistic domain, compare values (including endpoints when relevant).
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Translate English → diagram → constraint → objective → substitute → calculus.
Check units and whether a critical point is max or min (or nonsense physically).
Closed interval method: evaluate f at critical points and endpoints for absolute extrema.
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Attempt each problem first, then open the worked solution.
1.Maximize area of a rectangle with perimeter 40.