$(LocalMa\frac{x}{M}in)*$

Consider a function $f(x,y)=27x^3-8y^3+36x{y}^2-54x^{2}y-27x^2-12y^2+36xy+$

$9x-6y+11$ defined $on\{(x,y)$:$x\frac{1}{3},y0\}.$ Which $of$ the following $is$ true?

$(1)f$ has two stationary points.

$(2)11is$ a local maximum $off.$

$(3)f$ has a local maximum $at$ each critical point.

$(4)$ There $is$ a critical point $at$ which $f$ does not have a local maximum.

$(5)At$ each stationary point, the hessian matrix $offis$ negative definite.

$(1)$

$(2)$

$(3)$

$(4)$

$(5)$