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Discontinuous function at second derivative

  • Thread starter Applejacks
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Homework Statement



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

Homework Equations





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?
 

Answers and Replies

  • #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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