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Integral of f^4 f' Given Conditions

1800SpecialistCalculus

Harvard-MIT Mathematics Tournament

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 $\int_{0}^{1} f(x)^{4} f^{\prime}(x) d x$?
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