In calc I a function that is continuous on a closed interval is guaranteed to have an absolute maximum and an absolute minimum value on the interval. We'll chat about analogs to closed intervals in $\mathbb{R}^2$ and $\mathbb{R}^3$. And, we'll solve some problems (12.9) using gradient vectors to find the extreme value(s) of various functions on sets of points in both $\mathbb{R}^2$ and $\mathbb{R}^3$. A tiny amount calculus will occur.