Worked examples

Unconstrained and constrained extrema

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Stationary points and the Hessian test
• 2Absolute maxima and minima on closed and bounded sets
• 3Constrained extrema with Lagrange multipliers
• 4Stationary points of functions with exponentials and logarithms
• 5Stationary points with zero Hessian determinant
• 6Constrained extrema with the substitution method
• 7Maximum profit with two goods or two factors
• 8Consumer's problem and minimum-cost problem