Critical Points - Multivariable Calc

[Mona1990]

Hi, i was wondering if someone could please help to find and classify the critical points of :
f(x,y) = (x-y)^2

What i know:
I got fx = 2(x-y) and fy = -2(x-y)
and in order to find the critical points we need to solve:

2(x-y) =0
-2(x-y) = 0

so if x =y then the above hold.

where would I go on from here on?

thanks!

 

[zcd]

Basically anything that runs along the line y=x would contain your critical points. Plug y=x into the hessian matrix and then determine what kind of extrema it is.

 

[Mona1990]

Alright! thanks a lot :D