2730.sagews

This shows a portion of $2/x+2/y+xy$ around the only critical point. You may want to view a larger portion of the surface by changing the bounds on $x$ and $y$, say to $(x,0.1,5)$ and $(y,0.1,5)$, to get a better idea of the surface. The critical point is shown in red.

(x,y)=var("x y"); plot3d(2/x+2/y+x*y,(x,2^(1/3)-0.5,2),(y,2^(1/3)-0.5,2))+point3d((2^(1/3),2^(1/3),3*2^(2/3)),color='red')