Does the function $$f(x,y) = \frac{x^{2}}{2}+3y^{3}+6y^{2}-3x$$ have a global maximum and global minimum? If it does, identify the value of the maximum and minimum. If it does not, be sure that you are able to explain why.

Global maximum?
(Enter the value of the global maximum, or none if there is no global maximum.)
Global minimum?
(Enter the value of the global minimum, or none if there is no global minimum.)