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Answer whether the following statements are True or False.

Let $f:[0,1] \rightarrow[0, \infty)$ be continuous on $[0,1]$ and twice differentiable in $(0,1)$. If $f^{\prime \prime}(x)=7 f(x)$ for all $x \in(0,1)$, then $f(x) \leq \max \{f(0), f(1)\}$ for all $x \in[0,1]$.

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