I need to prove, that $5n^2+7=O(2^n)$
I came up with the following proof, is this correct?
To prove this, we need to show $5n^2+7 \le c*2^n$ for $n \ge b$
We know, that $7\le n^2$ for ever $n\ge3$ (Can we just assume this or do we have to prove it?)
Thus, we get $5n^2 + n^2 < c*2^n$ After minimizing the left side, we get $6n^2 \le c*2^n$
We know, that $n^2 \le 2^n$ for every $n \ge 4$ Thus, we get $6*2^n \le c*2^n$ for every $n\ge4$
So we can conclude, that our b is 4 and our c is 6.
Is this proof correct?