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Connecting Differentiability and Continuity

AP Calculus AB· difficulty 3/5

x x=2

At x=2x = 2, ff has a sharp corner. Which is true?

  • A

    f′(2)=0f'(2) = 0

  • B

    ff is discontinuous

  • C

    f′(2)>0f'(2) > 0

  • D

    f′(2)f'(2) does not exist

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Explanation

Left and right derivatives differ at the corner, so f′(2)f'(2) does not exist.

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