I've been given a question as follows: if Y is a non-negative random variable, I want to show that

$\displaystyle P(X\geq a)\leq e^{-ta}M(t)$,

where M(t) is the moment generating function of X. I think that Markov's inequality would be useful here, and I know that I can express E(X) as $\displaystyle M'(0)$, but I'm not sure how to do this without any more information about X and its mgf.

Any help would be appreciated!