Multivariable Optimization with Boundaries

Suppose we want to find the maximums and minimums of a function. Previously in our Calc III playlist we saw how to do this with the second derivative test. But what if we demand that are optimizing on a closed, bounded region? That is, a region that has a boundary. Similar to first year calculus, the idea is that the maximums and minimums either occur in the interior of the region (found by analyzing critical points with the second derivative test), OR the extrema occur along the boundary. In this video we will learn how to do this process along the boundary.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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