Differentiation of a Piecewise Function

In summary, the conversation discusses finding the second derivative of a graph of velocity vs time. The graph is described as a series of linear lines resembling a hill, with positive and constant dy/dx for a period of time before becoming zero and then negative. The solution proposed is to plot the derivatives of each part on the graph, even though it may not be continuous due to the nature of a piecewise function.
  • #1
GreenPrint
1,196
0

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

 
Physics news on Phys.org
  • #2
Plot the derivatives of each part on the graph. It may not be continuous, but it is a piecewise derivative. Can't expect continuity.
 

1. What is a piecewise function?

A piecewise function is a mathematical function that is defined by different equations or expressions for different intervals or domains of the independent variable.

2. What is the purpose of differentiating a piecewise function?

The purpose of differentiating a piecewise function is to find the slope or rate of change of the function at different points, which can be useful in analyzing and understanding the behavior of the function.

3. How do you differentiate a piecewise function?

To differentiate a piecewise function, you need to differentiate each piece of the function separately and then combine the results. This can be done using the power rule, product rule, quotient rule, or chain rule depending on the form of the function.

4. Can a piecewise function be differentiable at points of discontinuity?

No, a piecewise function cannot be differentiable at points of discontinuity since the derivative does not exist at these points. However, the function can still be differentiable on the intervals where it is continuous.

5. What are some real-life applications of differentiating piecewise functions?

Differentiation of piecewise functions has applications in many areas such as economics, physics, and engineering. For example, it can be used to analyze the marginal cost and revenue in economics, the velocity and acceleration of a moving object in physics, and the rate of change of temperature in engineering.

Similar threads

  • Calculus and Beyond Homework Help
Replies
9
Views
673
  • Calculus and Beyond Homework Help
Replies
4
Views
842
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
22
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
223
  • Calculus and Beyond Homework Help
Replies
26
Views
804
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
11
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
880
Back
Top