14.8

Second cell finds critical points.

Plug in critical points (one by one) into the third cell to compute the D quantity. If D is not zero, plug them into the 
fourth cell to find second partial in x. Use these two numbers to classify critical points. 

The fifth cell maximizes and minimizes f(x,y) on the rectangle [a,b] x [c,d]. If "Mathematica" can not do this analytically, 
use numerical analogs NMaximize and  NMinimize. Red point is the highest, blue the lowest.