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First and second derivatives

  1. Apr 30, 2010 #1

    I have been asked to find the first and second derivatives of lx-al-lx+al

    I have, for the first derivative got, sign(x-a)-sign(x+a)

    and for the second, i have: 2(delta)(x-a)-2(delta)(x+a)

    am i right in both cases?

    I also have to draw them 'schematically' how do i do this?
  2. jcsd
  3. Apr 30, 2010 #2


    Staff: Mentor

    You can rewrite your function formula without the absolution values, using a piecewise definition on three intervals: (-inf, -a], (-a, a] and (a, inf).

    For example, if x <= -a, |x - a| - |x + a| = -(x - a) - (-(x + a)) = -x + a + x +a = 2a.
    Do the same for the other two intervals.

    I don't know what "drawing them schematically" means, but a graph of the function would probably suffice.
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