ramification at infinity of a Galois Extension.

Question

Let $\mathbb F_q$ be a finite field, let $f\in \mathbb F_q[x]$, and let $t$ be trascendental over $\mathbb F_q$. Consider the splitting field $M$ of $f-t$ over $\mathbb F_q(t)$. Let $P_\infty$ be the place at infinity of $\mathbb F_q(t)$. Let $R$ be a place of $M$ lying over $P_\infty$. What can you say about the ramification of $R|P$? Clearly, it is divisible by $\deg(f)$ but how can one say more?