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$x = c$ is a critical number for $f(x)$. Which of the following must be true?

I. Either $f^\prime(c)=0$ or $f^\prime(c)$ does not exist.
II. The sign of the first derivative changes at $x = c$.
III. $f(c)$ is a local extreme value on $f(x)$.

A

I only.

B

I and II only.

C

II and III only.

D

I, II, and III.

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