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Homework Help: Solve |x-1|e^x

  1. Sep 28, 2005 #1
    Hi

    So Im a little confused about the absolute value sign here. Is the derivative right:

    [x-1/|x-1|]e^x + |x-1|e^x

    But what do I do when I set this to zero? Do I get two expressions, one for x>1 and one for x<1 ? (thus removing the absolute value signs)
     
  2. jcsd
  3. Sep 29, 2005 #2
    Hints anyone...?
     
  4. Sep 29, 2005 #3

    saltydog

    User Avatar
    Science Advisor
    Homework Helper

    [tex]|x-1|=x-1\quad\text{for}\quad x\geq 1[/tex]

    and:

    [tex]|x-1|=-(x-1)\quad\text{for}\quad x<1[/tex]

    Thus your expression represents this function:

    [tex]y(x)=
    \left\{
    \begin{array}{rcl}
    (x-1)e^x & \mbox{for} & x\geq 1 \\
    -(x-1)e^x & \mbox{for} & x<1
    \end{array}\right.
    [/tex]

    and so the derivative will represent two functions likewise but will not exist at x=1. Try plotting this conditional function and you'll see what I mean.
     
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