# How do you minimize and maximize #f(x,y)=x/y-xy# constrained to #0<x-y<1#?

##### 2 Answers

#### Explanation:

Both choices respect the constraint.

There is a local máxima at

#### Explanation:

Defining

and

the local maximization/minimization problem with inequality restrictions is transformed into an equivalent one, now with equality restrictions, so we can apply the Lagrange Multipliers technique for its resolution. The lagrangian is

Here

The stationary points are solutions of

or

Solving for

Here we observe that

Also we have

This result shows that the point