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Connecting Differentiability and Continuity

AP Calculus AB· difficulty 3/5

x cusp

At a cusp, the derivative:

  • A

    Equals the second derivative

  • B

    Equals one

  • C

    Equals zero

  • D

    Does not exist (one-sided slopes infinite)

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Explanation

At a cusp, slopes approach ±∞\pm\infty, so the derivative does not exist.

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