I've read all your posts, and reread them and there's something just no quite clicking. I need to prove, from first principals (which i'm not sure what first principles are), that:

f(x) = O(x^3) when given

f(x)=4x^3 - 3x^2 + 1

is this equivelant of the above equation or am i barking up the wrong post here?

p.s. and how do you get the superscript and subscript to work in these posts?