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Math Help - Differentiating an absolute value...

  1. #1
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    Unhappy Differentiating an absolute value...

    I love math, I really do, but differentiating absolute values is driving me crazy! I just don't get it, and the book does a terrible job explaining it. I have a test tomorrow which is guaranteed to have an absolute value differentiation question on it.

    I would truly appreciate it if someone could walk me through this example:

    Differentiate: y = |2x - 3|
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  2. #2
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    Re: Differentiating an absolute value...

    Quote Originally Posted by theunforgiven View Post
    I love math, I really do, but differentiating absolute values is driving me crazy! I just don't get it, and the book does a terrible job explaining it. I have a test tomorrow which is guaranteed to have an absolute value differentiation question on it.

    I would truly appreciate it if someone could walk me through this example:

    Differentiate: y = |2x - 3|
    First of all, \displaystyle \begin{align*} |X| = \begin{cases} \phantom{-}X \textrm{ if } X \geq 0 \\ -X \textrm{ if } X < 0  \end{cases} \end{align*} and also note that \displaystyle \begin{align*} |X| \end{align*} is NOT differentiable at \displaystyle \begin{align*} X = 0 \end{align*}.

    So for your function

    \displaystyle \begin{align*} y &= \left| 2x - 3 \right| \\ &= \begin{cases} 2x - 3 \textrm{ if } 2x - 3 \geq 0 \\ -\left( 2x - 3 \right) \textrm{ if } 2x - 3 < 0  \end{cases} \\ &= \begin{cases} 2x - 3 \textrm{ if } x \geq \frac{3}{2} \\ 3 - 2x \textrm{ if } x < \frac{3}{2} \end{cases} \end{align*}

    So differentiate each piece, and remember that the function won't be differentiable at \displaystyle \begin{align*} x = \frac{3}{2} \end{align*}.
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    Re: Differentiating an absolute value...

    Quote Originally Posted by theunforgiven View Post
    I would truly appreciate it if someone could walk me through this example:
    Differentiate: y = |2x - 3|
    Graph this.

    What are the slops?
    Attached Thumbnails Attached Thumbnails Differentiating an absolute value...-untitled.gif  
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