Order of $f(n) = 4n + 6n^3 - 8n^5$ If a function $$f(n) = 4n + 6n^3 - 8n^5$$ then the order of $f$ is:
The answer I have is $\log(n)$, but I'm not sure if it's right.

Let
$f: \mathbb{N} \to \mathbb{R}$
be the function
$$f(n) := 4n + 6n^{3} - 8n^{5}.$$
There are two possibilities:
1) $f(n) = o(n^{6}),$
for we have
$$\frac{f(n)}{n^{6}} \to 0$$
as $n \to \infty.$
2) $f(n) = O(n^{5}),$
for we have
$$\frac{f(n)}{n^{5}} < -7$$
eventually.
