HMMT 2005 K4

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a smooth function such that $f^{\prime}(x)^{2}=f(x) f^{\prime \prime}(x)$ for all $x$. Suppose $f(0)=1$ and $f^{(4)}(0)=9$. Find all possible values of $f^{\prime}(0)$.