Results 1 to 2 of 2

Thread: example of a function that is continuous but not differentiable

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    27

    example of a function that is continuous but not differentiable

    I need an example of a function that is continuous at some x0 but not differentiable at x0.

    is f(x) = |x| a right answer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    22
    Quote Originally Posted by dgmath View Post
    I need an example of a function that is continuous at some x0 but not differentiable at x0.

    is f(x) = |x| a right answer?
    Yes. Or a uniformly continuous function which is nowhere differentiable. In fact, given a continuous function $\displaystyle f:I\to\mathbb{R}$ you may construct a continuous function $\displaystyle g:I\to\mathbb{R}$ such that $\displaystyle \|f-g\|_{\infty}<\varepsilon$ for some fixed but arbitrary $\displaystyle \varepsilon>0$ and which is nowhere differentiable. Your answer also shows that given a function $\displaystyle f$ which is differentiable at $\displaystyle x_0$ that the function $\displaystyle f(x)+|x-x_0|$ is not differentiable at $\displaystyle x=x_0$ giving and infinitely weaker form of the aforementioned theorem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Oct 3rd 2010, 07:03 AM
  2. showing a function is continuous and differentiable
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: Apr 22nd 2010, 06:00 PM
  3. Differentiable, continuous function... "show that"
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 21st 2009, 03:01 AM
  4. Replies: 5
    Last Post: Dec 4th 2008, 08:18 AM
  5. continuous, not differentiable
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 22nd 2008, 02:56 PM

Search Tags


/mathhelpforum @mathhelpforum