Discontinuous function at second derivative

[Applejacks]

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?

 

[SammyS]

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 .