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AP® Calculus AB-BC

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Definition of Differentiability

APCALC-Z9XJGD

Given that a function is differentiable for all values of $x$, which of the following statements is not true?

A

There are no corners, cusps, or vertical tangents in the graph of the function.

B

There are no corners, cusps, or vertical tangents in the graph of the derivative of the original function.

C

The function is continuous for all values of $x$.

D

The limit of the function exists for all values of $x$.