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Math Help - differentiation of a modulus function

  1. #1
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    differentiation of a modulus function

    I'm a little confused

    f(x) = |x|^2 - 4|x|

    I know that gives the equations of:
    x^2 - 4x and
    x^2 + 4x

    and you can differentiate them, but which equation corresponds to which part of the graph?

    Thanks in advance
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by freswood
    I'm a little confused

    f(x) = |x|^2 - 4|x|

    I know that gives the equations of:
    x^2 - 4x and
    x^2 + 4x

    and you can differentiate them, but which equation corresponds to which part of the graph?

    Thanks in advance
    When x\ge 0:

    |x|^2 - 4|x|=x^2-4x.

    When x\le 0:

    |x|^2 - 4|x|=x^2+4x.

    As a reality check you can always try plugging in numbers and seeing what
    you get.

    RonL
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  3. #3
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    Hello, freswood!

    Find the derivtive of: f(x) \:= \:|x|^2 - 4|x|
    This is equivalent to the piecewise function: f(x)\:=\:\left\{\begin{array}{cc} x^2 - 4x & x \geq 0 \\ x^2 + 4x & x < 0\end{array}

    Differentiate them for both cases.

    You can check your results against the graph.

    Code:
                          |
            *             |             *
                          |
             *            |            *
          - - * - - - - - * - - - - - * - -
             -4 *       * | *       * 4
                   * *    |    * *
                          |
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  4. #4
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Soroban
    Differentiate them for both cases.
    differention of |x|=|x|/x
    where x is not equal to 0
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  5. #5
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    Thanks!

    What confused me is that for something like |x^2 - 4x| one applies to y>0 and the other to y < 0.

    as in x < 0 U x > 4
    and 0<x<4

    Can anyone explain the difference between the two?
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