Max / min on closed, bounded sets

A lecture that discusses extreme values (maxima and minima) for functions of two variables on a closed and bounded set. The ideas rely on the fact that every continuous function must achieve a maximum value and a minimum value on such a set. In the interior of the set we apply the 2nd-derivative test, while a separate treatment is required on the boundary of the set.

[DrChrisTisdell]

Hi - you should check with your Prof. If you mean what happens if there is a critical point that doesn't lie within the interior or on the boundary of \Omega, then I would think it could be ignored.

[Hemenmyname]

Thanks, very clear and concise! Good explanations!