Exercise $2-$Minimum$($s$)/$Maximum$($s$)$

Find the local maximum and minimum values and saddle point$($s$)$ of the functions.

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

$(2)f(x,y)=\frac{x-y}{1+x^2+y^2},$

$(3)f(x,y)=x^2{e}^{-(x^2+y^2)}.$