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

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

critical point $($stationary point$)$: $(,)$

use $2$nd derivative test to evaluate $D(a,b)$ and $f_{}(a,b)$

$D(a,b)=$

$$

$f_{}(a,b)=$

$$

$f(a,b)=$

$$

nature of critical point: $($local max, local min, saddle$)$