# How do i determine maximum or minimum at (1,1) of function $f(x,y)=(x-y)^{4} + (y-1)^{4}$

How do i determine maximum or minimum at this point of function

$$f(x,y)=(x-y)^{4} + (y-1)^{4}$$

I am getting doubtful case at point (1,1). How do i furthure investigate whether it is point of minima or maxima

Thanks

Notice that you add $2$ non - negative terms! Thus, $f(x,y) \ge 0,$ for all $x,y \in \mathbb R$. For which $x,y$ does it hold $f(x,y) = 0$?