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

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

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

$$

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

$f_{}(a,b)=$

$$

$D(a,b)=$

$$

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

$f(a,b)=$

$$