Differentiation of a Piecewise Function

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SUMMARY

The discussion focuses on differentiating a piecewise function represented by a velocity vs. time graph. The graph consists of linear segments, indicating that the first derivative (velocity) is positive, zero, and then negative across different intervals. To find the second derivative (acceleration), one must compute the derivative for each linear segment separately, acknowledging that the overall derivative may not be continuous due to the nature of piecewise functions.

PREREQUISITES
  • Understanding of piecewise functions
  • Knowledge of basic calculus, specifically differentiation
  • Familiarity with graph interpretation
  • Concept of continuity in functions
NEXT STEPS
  • Learn how to differentiate piecewise functions effectively
  • Study the concept of continuity and its implications on derivatives
  • Explore graphical representation of derivatives for piecewise functions
  • Investigate applications of acceleration in physics
USEFUL FOR

Students studying calculus, particularly those working with piecewise functions and their applications in physics, such as velocity and acceleration analysis.

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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 derivative of the whole graph

Homework Equations





The Attempt at a Solution

 
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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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