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

##### 1 Answer

The function:

constrained by

has two local maximums for

#### Explanation:

From the constraint equation:

we can derive:

and substitute it in the original equation:

We can now find the local extrema for

The critical points are determined by the equation:

Looking at the sign of the derivative we can see that:

So that

so that also