Finding moment generator function, when the mean and variance are known

Question

Let's say I have this random variable $X$ with $E(X)=\mu$ and $Var(X)=\sigma^2$. How can I find the moment generating function? I know that $M'(0)=E(X)$, and that in general $M^{(k)}(0)=E(X^k)$. So I'd force $M'(0)=\mu$ and that $M''(0)=E(X^2)=\sigma^2+\mu^2$. How can I proceed?