Question

How do you minimize and maximize `f(x,y)=x-y/(x-y/(x-y))` constrained to `1<yx^2+xy^2<16`?

Answer 1

See below.

Explanation:

This problem can be successfully handled with the Lagrange Multipliers technique.

The local maxima/minima points are

#((f(x,y),x,y, "type"), (-0.750704,-1.71756,1.25284,"maximum"), (1.81974,0.562693,-1.64382,"minimum"), (-3.39363,-4.05723,2.44297,"maximum"), (3.33301,1.4188,-4.14166,"minimum"))#

Attached a plot showing the feasible region superimposed to the objective function level curves, with the local maxima/minima points.