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Math Help - Odd Question

  1. #1
    Newbie
    Joined
    Aug 2009
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    1

    Odd Question

    Aight, here's the question:

    "Using the definition of derivative, find the derivative of the following function:

    y= lxl (hint; rewrite this function as a piece-wise function first)"

    I have managed to write it as a piece-wise, but I'm not sure what I'm supposed to do from that point. Thanks in advance for any help!
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  2. #2
    Member
    Joined
    Aug 2009
    Posts
    130
    Just differentiate it piece-wise as well.

    You should have f(x) = |x| = x if x>=0 or f(x) = |x| = -x if x < 0.

    For x < 0 what will the derivative be? For x > 0 what will the derivative be? For x = 0, take a look at the graph of |x|. Does it look like the derivative will exist there? Also for x = 0, look at the one-sided limits for
    f(0 + h)/h
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