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Derivative of this piecewise function?

  1. Oct 2, 2011 #1
    1. The problem statement, all variables and given/known data
    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?



    2. Relevant 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| }


    3. 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?
     
  2. jcsd
  3. Oct 2, 2011 #2

    SammyS

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    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 !
     
  4. Oct 2, 2011 #3
    Oh right, I asked a little too quick before thinking it through enough.
    Thanks!
     
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