Difficult# Behavior of Second Derivative

APCALC-YUPBEX

If $f(x)$ is a differentiable function with a point of inflection at $x=2$, which of the following statements must be true?

I.$\quad { f }^{ \prime \prime }( 2 ) =0$.

II.$\quad { f }^{ \prime \prime }( x )$ changes sign at $x = 2$.

III.${ \quad f }^{ \prime }( x )$ has an extreme value at $x = 2$.