How can I show without induction that $n^3\geq 3n^2$ for $n\geq3$? ($n$ is a natural number).
$f(x)=x^3-3x^2\geq0$ for $x\geq 3$ so it follows that $n^3\geq 3n^2$ for $n\geq3$.
Any other solutions?
The inequality can be generalized as $f(x)\geq f'(x)$. Under what condition is this inequality true?