How to find witnesses for big O
In your case finding the witness is easy. We know that for all $x \geq 0$, $2^x \leq 3^x$. Also, for $x \geq 3$, $17 \leq 3^x$. So for $x \geq 3$, $2^x+17 \leq 2\cdot 3^x$.

There is no particular method at work here – just problem solving.