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Section 2.3 Optimization
Objectives
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Model objectives and constraints to set up optimization problems.
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Identify interior and boundary candidates using derivatives and Fermat’s theorem.
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Use the First Derivative Test to classify critical points as local maxima, local minima, or neither.
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Same modeling steps as in related rates
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Don’t necessarily need to eliminate variables — using differentials also works!
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Focus on absolute maxima and minima and ‘candidates’ using Fermat’s theorem: if
\(f\) has a local maximum at
\(x=a\text{,}\) then
\(f'(a)=0\)
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First and second derivative tests for optimization
