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Discontinuous function at second derivative

  1. Nov 4, 2011 #1
    1. The problem statement, all variables and given/known data

    http://imageshack.us/photo/my-images/717/unleddym.png/

    2. Relevant equations



    3. The attempt at a solution

    I was wondering why the second derivative at t=1 does not exist but exists at the first derivative. What I did was draw the graph of the function, then the first derivative and lastly the second derivative. I found that at t=1, the function and its first derivative agreed on both the left hand and right hand sides. However, at t=1 for the second derivative, the top part of the function was 2 and the bottom was 0. Is this why it's not continuous for t=1 at the second derivative?
     
  2. jcsd
  3. Nov 4, 2011 #2

    SammyS

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    The function and its first derivative are both continuous at t = 1, but the first derivative has a cusp at t = 1, so the second derivative does not exist at t = 1 .
     
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