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AP® Calculus AB-BC

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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 $x = 2$.

A

I only

B

II only

C

II and III only

D

I, II and III