Find the critical points for the function

$f(x,y)=x^3+y^3-12x^2-3y+3$

and classify each as a local maximum, local minimum, saddle point, or none of these.

critical points:

$($give your points as a comma separated list of $(x,y)$ coordinates.$)$

classifications:

$($give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points$)$