Worked examples

Free and constrained maxima and minima

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.

• 1Classification of critical points with the Hessian matrix
• 2Critical points of functions with exponentials and logarithms
• 3Critical points with a degenerate Hessian and direct study of the sign
• 4Absolute extrema on rectangles and triangles
• 5Absolute extrema on circles and disks
• 6Lagrange multipliers with one constraint
• 7Geometric optimization problems