# Finding global minumum maximum

How can I find the global min/max in this problem?
Find the critical points of the function :
f(x,y)=$2x^3-3x^2y-12x^2-3y^2$
and determine their type.
Are there any global min/max?

The critical points were: (0,0), (2,-2),(-4,-8) By using the hessian matrix I found their types:
(0,0) is a local maximum
(-4,-8) is a saddle
(2,-2) is a saddle.

But I do not understand how to find the global minimum or maximum.
I know that if the Hessian matrix is negative semi definite then any local max is a global max and if Hessian matrix is a positive semi definite then any local min is a global min.

There isn't a global maximum or minimum, at least not when considered on $\mathbb{R}^{2}$. Set $y=0$ and you can easily see that your function neither has an upper nor lower bound.
Note that the highest power of $x$ is 3. So if you make $x$ large positive then $f$ is also large positive (just set $y=0$). Similarly if you make $x$ large negative, $f$ will be large negative.