Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
  5. Sep 28, 2004 #4

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

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    To give you another one:
    Define f(x) as:
    [tex]f(x)=\sum_{n=0}^{\infty}\frac{\sin((n!)^{2}x)}{n!}[/tex]
    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

    Pyrrhus

    User Avatar
    Homework Helper

    It means Factorial, look it up.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook