Understanding negative definite/semidefinite functions

Question

I'm working on control theory and have some difficulty understanding if a function is negative definite or semidefinite.

Given the system

$\dot{x_1} = -x_2^2$

$\dot{x_2} = -x_1^2x_2 + x_1^3 - x_2$

How do I determine if

$-x_1^2x_2^4 - x_2^4$

is negative definite or negative semidefinite?

Answer 1

Is there $(x_1, x_2) \neq (0,0)$ such that the function attains $0$? If so, it is semidefinite.

Note that I don't know your definition, I'm just guessing by the usual definition for bilinear forms.