# Math Help - Proof by first principles

1. ## Proof by first principles

I think i got this right, not sure. Please check for me.

Let f: R--->R be given by

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

Prove from first principles, that f(x)= O(x^3)

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

<=4x^3 -3x^3 + x^3=2x^3

So, does me saying f(x)<=2g(x^3) provide proof? or is there something else i have to do?

2. Not quite right, check your other thread where you asked this. I answered there.

Your inequalities are not true here actually.

It is not true that $4x^3 - 3x^2 \leq 4x^3 -3x^3$ even for like 2 it fails, so you gotta be a little careful there. You need to make the sign positive, just check the other post.