Graphing a Piecewise Function: Is it Continuous and Differential?

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SUMMARY

The discussion focuses on graphing a piecewise function to determine its continuity and differentiability. The function is defined in two segments: for r ≤ r0, it is represented by a straight line with a slope of B0/r0, and for r > r0, it is defined as r0B0/r. Participants emphasize the importance of accurately sketching both segments on the same graph to analyze the function's characteristics effectively.

PREREQUISITES
  • Understanding of piecewise functions
  • Knowledge of continuity and differentiability in calculus
  • Ability to graph linear equations
  • Familiarity with slope-intercept form
NEXT STEPS
  • Study the properties of piecewise functions in calculus
  • Learn how to determine continuity and differentiability at transition points
  • Practice graphing piecewise functions with different slopes
  • Explore the implications of discontinuities on function behavior
USEFUL FOR

Students studying calculus, particularly those focusing on piecewise functions, continuity, and differentiability. This discussion is beneficial for anyone needing assistance with graphing techniques in calculus.

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Homework Statement


This is the last of 10 calculus problems I have to do this week (besides the one I have half finished) 7/8 so far :). This problem asks if the function is continuous and differential. I don't know how to graph this though. Can somebody help explain, I only need to know how to sketch a graph of this.

http://img27.imageshack.us/img27/5519/picture1tz.png

Thanks.


Homework Equations





The Attempt at a Solution

 
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Call the x-axis the r axis and the y-axis the B axis, so you are going to graph B as a function of r. Label a point r0 on the r axis and a point B0 on the B axis.

Now for r ≤ r0 you have a straight line with slope B0/r0. And for r > 0 you have r0B0/r). Just sketch the two pieces on the same graph.
 

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