I need to determine whether the fct has any local minimums and/or maximums.

$\displaystyle f(x,y)=x^2-2xy+y^2$

I optimized and found that the f.o.c gives: x=y (right?). Does that mean that at ALL constants, c, where x=y=c, we have a local minima? Or does this mean that the function doesn't have any optimal values?

tks