Chapter 14.7, Problem 39E

To determine

The maximum of $f\left(x,y\right)=x+y-x^2-y^2-xy$ on the square $0\le x\le 2,0\le y\le 2$

(a) The critical point of $f$ on the square and evaluate $f$ at this point.

(b) The extreme value of $f$ on the bottom edge.

(c) The extreme value of $f$ on the remaining edges.

(d) The largest among the values computed in $\left(a\right),\left(b\right)\text{and}\left(c\right)$.