Differentiation of a Piecewise Function

[GreenPrint]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Char. Limit]

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