(*^

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:[font = special1; inactive; preserveAspect; ]
                              Optimizing a Function of Several Variables

The following cell illustrates how Mathematica  can do all the work involved in simple optimization problems like the example and the Check Your Understanding problems in this module.  Evaluate it now. 
;[s]
6:0,1;72,0;109,2;120,0;259,3;274,0;277,-1;
4:3,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[x, y, F, Fx, Fy]

F[x_, y_] := 2*x*y + 2/y + 2/x

Fx[x_, y_] = D[F[x, y], x]
Fy[x_, y_] = D[F[x, y], y]

Solve[{Fx[x, y] == 0, Fy[x, y] == 0}, {x,y}] 
:[font = special1; inactive; preserveAspect; ]
The following cell illustrates the way in which Mathematica  can graph a function of two variables.  Evaluate it now.
;[s]
5:0,0;48,1;59,0;101,2;116,0;118,-1;
3:3,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Plot3D[x^2 + y^2, 
     {x, -1, 1}, {y, -1, 1}]
^*)