Calculus I · 2B · review
Optimization Review
Review optimization review with mixed practice and links back to the exact lessons behind each skill.
Section overview
OptimizationWhat this section is building
Review optimization review with mixed practice and links back to the exact lessons behind each skill.
Optimization is a modeling problem first: the derivative only compares candidates after the geometry, units, and feasible domain are correct.
Write variables and units, identify the objective, use the constraint to eliminate a variable, then test critical and boundary candidates.
Optimizing the constraint, ignoring the feasible domain, or keeping an algebraic critical point that cannot exist in the real design.
Optimization Review
Optimization requires an objective, a constraint, a one-variable model, a feasible domain, critical numbers, endpoints, and an interpretation. A derivative locates candidates; comparison and context determine the answer.
Find the rectangle of maximum area with perimeter .
Exercise 1 answer
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A farmer has m of fencing for three sides of a rectangle beside a river. Maximize area.
Exercise 2 answer
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Find the dimensions of a closed cylinder of fixed volume using minimum material.
Exercise 3 answer
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Find the point on closest to .
Exercise 4 answer
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Maximize on .
Exercise 5 answer
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Design a gutter by folding equal edges of a strip and maximize cross-sectional area.
Exercise 6 answer
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Explain why minimizing distance squared gives the same location as minimizing distance.
Exercise 7 answer
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Write a full model for the Norman window problem and identify its feasible domain.
Exercise 8 answer
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