Prove or refute $f(n) * g(n) \ge f(n) + g(n)$ I received some homework (calculus), which I can't prove:
$f(n) * g(n) \ge f(n) + g(n)$ for some $n \geq 1$ is always true $(f(n),  g(n) \ge 1)$

I think that this is true, so I need to prove that there is some $n \geq 1$ ($n$ is a natural number) for which this inequality will be true always, thanks in advance for any idea
Hint: $2.25 &lt; 3$.
If $f$ and $g$ are both constant functions, then it's easy to see that the claim isn't true in general. Let's assume that $g$ is not constant, and since this problem came from a calculus class, let's assume that $f$ and $g$ are differentiable. Compare the derivative of $f(x) \cdot g(x)$ with the derivative of $f(x) + g(x)$. What can you say about the relative size of the derivatives? What does that tell you about the functions?