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1. The problem statement, all variables and given/known data

Find all critical points of the function

f(x, y) = xy^{2}- 2xy - 2x^{2}- 3x +7

and determine their nature.

2. Relevant equations

none

3. 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.

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# Finding the critical point and its nature. With solid attempt

**Physics Forums | Science Articles, Homework Help, Discussion**