Let $\displaystyle f$ be defined on an interval $\displaystyle I$ of length at least 2 and suppose that $\displaystyle f^{''}$ exists there. If $\displaystyle \vert f(x) \vert \leq 1$ and $\displaystyle \vert f^{''}(x) \vert \leq 1$ for all $\displaystyle x \in I$ show that $\displaystyle \vert f^{'}(x) \vert \leq 2$ on the interval.