Derivative of this piecewise function?

[Inertigratus]

Homework Statement

I have this piecewise defined function and am wondering if the derivative is supposed to be piecewise defined as well?
Or could I just write it out on a line like a "normal" function?

Homework Equations

x(t) = {-14t : 0[itex]\leq[/itex]|t|< 1, 2sgn(t) : 1[itex]\leq[/itex]|t|< 7, (-12/7)sgn(t) : 7[itex]\leq[/itex]|t|< 14, 0 : 14[itex]\leq[/itex]|t| }

The Attempt at a Solution

I'm thinking I can write the derivative as a normal function. Since the piecewise functions are defined with no time-jumps between them and the derivative will have Dirac delta functions defined at the function incontinuities. Therefor the derivative should be continuous on the interval:
0[itex]\leq[/itex]|t|[itex]\leq[/itex]14.
Is this correct?

 

[SammyS]

Graph the function.

That should tell you the answer.

There are no gaps in the function definition -- if you are referring to the fact that the domain of the function is (-∞, ∞). However, this function has discontinuities at several places. Its derivative has even more discontinuities than the function itself !

 

[Inertigratus]

Oh right, I asked a little too quick before thinking it through enough.
Thanks!