Consider the function

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

Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank.

$f_x=$

$f_y=$

$f_{xz}=$

$f_{xy}=$

$f_{xy}=$

The critical point with the smallest $x-$coordinate is

$$ Classification: $($local minimum, local maximum, saddle point, cannot be determined$)$

The critical point with the next smallest $x-$coordinate is

$$ Classification $($local minimum, local maximum, saddle point, cannot be determined$)$

The critical point with the next smallest $x-$coordinate is

$$ Classification: $($local minimum, local maximum, saddle point, cannot be determined$)$