Algorithm analysis, finding a constant c and a point n? Say for example I say that:
$$
2n^2 + n - 8 \quad\text{is}\quad O(n^3)
$$
To prove this I must find a constant $c$ and a point $n_0$ for which $n^3$ is an upper bound of the equation.
This is easy to see because $n^3$ will always be larger than $2n^2$ (dominant term) for any constant $c$. How do I find $n_0$?

The $-8$ makes the examples harder to see, so I will ignore it.  As you say, you want to choose $c$ and $n_0$ so that $n \gt n_0 \implies cn^3 \gt 2n^2+n$.  You get to choose $c$ and $n_0$ and there are many choices that will work.  One choice would be $c=1$, in which case you can show that $n_0=2$ (or anything larger) will work.  Also, you could choose $n_0=0,$  in which case $c$ needs to be at least $4$.
