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Continous function

  1. Sep 27, 2004 #1
    continuous function

    Is there a continuous function that has no tangent line at all? If so what is it? I know it must be made up of cusps and corners
    Last edited: Sep 28, 2004
  2. jcsd
  3. Sep 28, 2004 #2
    A function that doesn't have a tangent at a point means that the function's derivative doesn't exist at that point. You're right, functions are non-differentiable at cusps or corners. Examples of functions that don't have derivatives at one or more points include the absolute value function: [tex]y = \left|x\right|[/tex] or the Heaviside step function: [tex]\theta(x) = \left\{\begin{array}{cc}0,&\mbox{ if }
    x\leq 0\\1, & \mbox{ if } x>0\end{array}\right.[/tex]
  4. Sep 28, 2004 #3
    A function can be nowhere differentiable yet everywhere continuous. It's hard to draw but it does exist. Here is an example

  5. Sep 28, 2004 #4

    That cleared it up but i couldnt figure out the equation of the function.
  6. Sep 28, 2004 #5


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    Dearly Missed

    To give you another one:
    Define f(x) as:
    f'(x) cannot be defined at any point, although f(x) is continuous for all x.
    This is, I believe, Weierstrass' first published example of such a function.
  7. Sep 28, 2004 #6
    What does the n! stand for
  8. Sep 28, 2004 #7


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    It means Factorial, look it up.
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