Connecting Differentiability and Continuity

AP Calculus AB· difficulty 2/5

Which is true?

  • A

    Continuous ⇒ differentiable

  • B

    Differentiable ⇔ continuous

  • C

    Differentiable ⇒ continuous

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  • D

    Neither implies the other

Explanation

Differentiability implies continuity (but not the reverse: x|x| is continuous but not differentiable at 00).

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