Answer
Saddle point at $(0,0)$
Work Step by Step
Since, we have $f_x(x,y)=2x+2y=0, f_y(x,y)=2x=0$
After solving the above two equations, we get
$x=0,y=0$
Thus the critical point is: $(0,0)$
As per second derivative test, we have
$D=f_{xx}f_{yy}-f^2_{xy}=-4$ and $D=-4 \lt 0$
Thus, saddle point at $(0,0)$
