Results 1 to 2 of 2

Math Help - show that h is differentiable everywhere and that h' is continuous everywhere but....

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    133

    show that h is differentiable everywhere and that h' is continuous everywhere but....

    Define h(x)=x^3sin(1/x) for x not equal to 0 and h(0)=0. Show that h is differentiable everywhere and that h' is continuous everywhere but fails to have a derivative at one point.

    I have h'(x) to be : (3 x^2) sin(1/x)-x cos(1/x) but im i don't know how to show what is being asked.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,560
    Thanks
    1425
    To be continuous everywhere, at the possible point of discontinuity, if the left hand limit and right hand limit are equal to the function at that point, then the function is continuous everywhere.

    To be differentiable everywhere, at the possible point of no-differentiability, the left and right hand limits of the derivative at that point have to be equal.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. continuous/differentiable
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 8th 2010, 09:19 AM
  2. Replies: 0
    Last Post: October 3rd 2010, 07:03 AM
  3. Continuous but not differentiable
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 1st 2009, 10:24 AM
  4. Differentiable, continuous function... "show that"
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 21st 2009, 03:01 AM
  5. continuous, not differentiable
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 22nd 2008, 02:56 PM

Search Tags


/mathhelpforum @mathhelpforum