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I Not quite a discontinuity?

  1. Jan 27, 2017 #1
    For example, if we define f(x) as "the greater of x and x2" it will give a straight line graph between (0,0) and (1,1) then turn into a curve. This function is continuous but not 'smooth'.

    Is there any special name for this kind of function?

    Are there any interesting considerations about such functions - or is it just a case of 'split them up into parts when necessary'?
     
  2. jcsd
  3. Jan 27, 2017 #2

    mfb

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    2016 Award

    Staff: Mentor

    "Continuous but not differentiable"?
    There are functions continuous everywhere, but not differentiable anywhere (e. g. the Weierstrass function).
    Smooth is a mathematical term, and requires derivatives of all orders to exist.
     
  4. Jan 27, 2017 #3

    Stephen Tashi

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    The adjective "piecewise" could be used. (https://en.wikipedia.org/wiki/Piecewise ). You could say the function is "piecewise smooth".
     
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