Moderate# Mean Value Theorem & Continuity

APCALC-GCJMZS

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 $[a,b]$.