# How do you minimize and maximize #f(x,y)=(x-y)/((x-2)^2(y-4))# constrained to #xy=3#?

##### 1 Answer

Local maximum located at

#### Explanation:

We will be looking for stationary points with posterior qualification.

This technique consists in finding points such that the normal vector to the objective function

and the restriction function

are aligned. Formally speaking, there exists

proceeding this way we obtain the equation set

Without much effort can be obtained the unique real solution

Qualifying this point must be done considering the restriction so the easiest way to do that is substituting the restriction

objective function

then we can verify that

and

qualifying this point as a local maximum.

Attached are two figures. One representing the surface intersection of