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Differentiation of a Piecewise Function

  1. Jul 27, 2010 #1
    1. The problem statement, all variables and given/known data
    I have a graph of velocity vs time and was asked
    "Describe how the velocity changes over the time interval of the problem"
    how do I do this all I have is the graph that is not defined by a function... well I can make my own strangely all it is is a bunch of linear lines put together that looks like this
    .._
    /...\

    sort of like a hill were it dy/dx is positive and constant for bit then is zero for a while then becomes negative so I wanted to find the second derivative of this, acceleration, not exactly sure how to do this with a piecewise funciton this is what it is now? I have to come up with the derivative of each part and then what should i do to come up with the derivitive of the whole graph

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 27, 2010 #2

    Char. Limit

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    Gold Member

    Plot the derivatives of each part on the graph. It may not be continuous, but it is a piecewise derivative. Can't expect continuity.
     
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