?

AP® Calculus AB-BC

Free Version

Upgrade subject to access all content

Easy

Critical Numbers

APCALC-ZLE4SX

$x = c$ 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