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**Finding the critical point and its nature. With solid attempt!**

## Homework Statement

Find all critical points of the function

f(x, y) = xy

^{2}- 2xy - 2x

^{2}- 3x +7

and determine their nature.

## Homework Equations

none

## The Attempt at a Solution

I know that to find the critical points you must set f

_{x}= 0 and f

_{y}=0

Doing this I get:

f

_{x}= -4x + y

^{2}- 2y - 3 = 0

and

f

_{y}= 2xy - 2x = 0

Thus, f

_{x}= f

_{y}

-4x + y

^{2}-2y - 3 = 0

-4x + (y+1)(y-3) = 0

I don't really know how to proceed? Any help would be great.