Show the absolute value of a function is not differentiable?

Show y=|x-2| is not differentiable at x=2, by showing that the limit in the definition of the derivative does not exist

2 Answers

Relevance
  • 5 months ago

    y=|x-2|=x-2, when x>2

    y=|x-2|=0, when x=2

    y=|x-2|=-x+2, when x<2

    Consider

    limit [(2-2+h)-(2-2)]/h=1

    h->0+

    limit [-(2+h-2)-(-2+2)]/h=-1

    h->0-

    Since the limits are not equal,

    the derivative of y at x=2 does

    not exist.

  • Amy
    Lv 7
    5 months ago

    The problem tells you what to do.

    Start with the definition of a derivative. Fill in y = |x-2| and x=2.

    After you cancel out all the 2's, you're left with a fairly simple limit statement. Try to evaluate that limit from both directions.

    Why does the limit not exist?

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