Question

How do you minimize and maximize `f(x,y)=(x-y)/(x^2+y^2)` constrained to `0<xy-y^2<5`?

Answer 1

See below.

Explanation:

Local maxima/minima can be located using the Lagrange Multipliers technique. The attached figure shows the two stationary points with local maxima/minima, at the feasible region border. The arrows show the objective function gradient direction at those points.

`((f(x,y),x,y),(-0.137852,-5.44061,-1.17109),(0.137852,5.44061,1.17109))`