If the Mean Value Theorem can be applied for the function $f(x)$ on the interval $(a,b)$ which of the following conditions must be true?

I.$f(x)$ is continuous on the interval $[a,b]$.II.$f(x)$ has at least one zero on the interval $(a,b)$.III.$f(x)$ is differentiable on the interval $[a,b]$.

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