so i have a function

$\displaystyle f(x,y) = x^2+3y^2-y^3+5$

I want to find the stationary point

$\displaystyle f_x = 2 , f_y = 6y-3y^2$

so stationary point is at (0,2) ??

Then to find if its a max or min

$\displaystyle f_{xx} = 2 , f_{yy}=6-6y , f_{xy}=0 $

So $\displaystyle f_{xx}f_{yy}-f_{xy}^2 = 2 \cdot (6-6y)-(0)^2= 12-12y$

So do i then sub in my value for y e.g y = 2 so ifnd out what that answer is? Or have i done something wrong?