Question

How do you maximize and minimize `f(x,y)=1/(xy)` constrained to `2<x^2+y<4`?

Answer 1

See below.

Explanation:

Using the technique of Lagrange Multipliers to locate the stationary points we obtain the solution about the local minima/maxima.

The attached plot shows the local minima/maxima points at the feasible region boundary.

`((f(x,y), x, y,"type"),(-0.918559,-0.816497,1.33333,max),(0.918559,0.816497,1.33333,min),(-0.32476,-1.1547,2.66667,max),(0.32476,1.1547,2.66667,min))`