Multivariable Calculus, Class #26, Optimization of a Continuous Function on a Compact Set

A continuous function f(x,y) is optimized over two separate closed and bounded (compact) domains. The critical points in the interior of the domain are classified, and the function is also analyzed along the boundary (using polar coordinates for the 2nd domain). The Method of Lagrange Multipliers is overviewed without getting into algebraic details.