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Example a function that is continuous at every point but not derivable

  1. Jul 14, 2008 #1
    can you example a function that is continuous at every point but not derivable
     
  2. jcsd
  3. Jul 14, 2008 #2
    Re: function

    The slope erratically changes.
     
  4. Jul 14, 2008 #3
  5. Jul 15, 2008 #4
    Re: function

    Yes, I also think of the weierstrass function is a perfect example of that.
     
  6. Jul 15, 2008 #5
    Re: function

    I was thinking the dirichlet function, but that's the one that's discontinuous everywhere.
     
  7. Jul 16, 2008 #6
    Re: function

    [tex]f(x)= sin (\fraction\pi/x)[/tex]
    [tex]f(x) = |x|[/tex]
    The problem's ambiguity at x=0.

    Any interval on a curve where the derivative would divide by zero. [tex]f(x) = \sqrt[3]{x}[/tex] would do this at x=0.

    Edit* I'm sorry if you were looking for functions that are not differentiable on any interval but are continuous.
     
    Last edited: Jul 16, 2008
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