HMMT 2005 K3

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function with $\int_{0}^{1} f(x) f^{\prime}(x) d x=0$ and $\int_{0}^{1} f(x)^{2} f^{\prime}(x) d x=$ 18. What is $\int_{0}^{1} f(x)^{4} f^{\prime}(x) d x$ ?