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Math Help - Derivatives #2

  1. #1
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    Exclamation Derivatives #2

    Find the derivative of y=|x|+|x-1|
    Last edited by mr fantastic; October 16th 2009 at 02:36 AM. Reason: Edited post title
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  2. #2
    MHF Contributor red_dog's Avatar
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    y=\left\{\begin{array}{lll}-2x+1, & x<0\\1, & x\in(0,1)\\2x-1, & x>1\end{array}\right.

    Then y'=\left\{\begin{array}{lll}-2, & x<0\\0, & x\in(0,1)\\2, & x>1\end{array}\right.

    y is not differentiable for x=0 and x=1.
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  3. #3
    MHF Contributor chisigma's Avatar
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    Because...

    y=|x| \rightarrow y^{'} = \left \{\begin {array}{cc}-1, &\mbox{if } x<0\\ 1,& \mbox{if } x>0\end{array}\right.

    y=|x-1| \rightarrow y^{'} = \left \{\begin {array}{cc}-1, &\mbox{if } x<1\\1,& \mbox{if } x>1\end{array}\right.

    ... is...

    y=|x| + |x-1| \rightarrow y^{'} = \left \{\begin {array}{cc}-2, &\mbox{if } x<0\\0,& \mbox{if } 0<x<1\\2, &\mbox{if } x>1\end{array}\right.

    Kind regards

    \chi \sigma
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