How can you show that the f distribution goes to zero as x approaches infinity
The pdf has the form $\displaystyle f(x) = C \, \frac{x^{\frac{n}{2} - 1}}{(M + nx)^{\frac{n+m}{2}}}$ where $\displaystyle C$ is a constant.
1. Solve $\displaystyle f'(x) = 0$. I suggest using the quotient rule to get the derivative.
2. I suggest you first substitute some concrete values for $\displaystyle m$ and $\displaystyle n$ and then attempt taking the limit. This will let you get the feel of things.