= Solution
Write $f(x,y)=g(x)+g(y)$ with $g(s)=s^3/12-s$. On $[0,4]$, its <derivative> is $g'(s)=s^2/4-1$, negative below two and positive above two. Compare the critical and endpoint values:
$$
g(0)=0,\qquad g(2)=-\frac43,\qquad g(4)=\frac43.
$$
Each coordinate can be chosen independently. Therefore \b[the global minimum is $-8/3$ at $(2,2)$, and the global maximum is $8/3$ at $(4,4)$]. This comparison includes the boundary of the rectangle, rather than classifying only interior <stationary points>.
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