Consider the function of 2 variables $\displaystyle F(x,y)=21x-12x^2-2y^2+x^3+xy^2$

Find the points of local minimum.

And show that F has no global minimum.

For the 1st part, I have obtained x=2, and correspondingly the value of y. But how to show the 2nd part? Am I to show F takes $\displaystyle -\infty$ as minimum value?

Don't know whether the answer of 1st part is needed to solve the 2nd part.

Help needed....