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AP® Calculus AB-BC

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Understand Ways to Mess Up Differentiability

APCALC-5OYEGL

If $g(x)$ is continuous on the interval $[a,b]$ but $g’(c)$ does not exist for some value of $c$ in the interval $(a,b)$, which of the following could be true?

A

$x=c$ is a vertical asymptote of the graph of $g(x)$.

B

The graph of $g(x)$ has a corner at $x=c$.

C

$g(c)$ does not exist.

D

$\lim \limits_{x \to c^-} g(x) \neq \lim \limits_{x \to c^+} g(x)$