Results 1 to 2 of 2

Math Help - Is this Function C^2?

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    22

    Is this Function C^2?

    Hello,

    given the following function from R^2 to R^2:

    f(x,y)=1/(x^2+y^2) * (x,y) if (x,y) not (0,0)
    f(x,y)=0 if (x,y)=(0,0)

    Is that function C^2 (= 2 times continuously differentiable)?

    A yes/no answer would be enough.

    Regards,
    engmaths
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,881
    Thanks
    697

    Re: Is this Function C^2?

    Hey engmaths.

    Do you need to differentiate it over the entire R^2 region? If you need to do this then you can show that you have a discontinuity and hence it is not differentiable.

    If you exclude this point, then show that the function is differentiable (using the definition) and apply it again for the first derivative.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 20
    Last Post: November 27th 2012, 05:28 AM
  2. Replies: 3
    Last Post: September 8th 2012, 04:00 AM
  3. Replies: 0
    Last Post: October 19th 2011, 04:49 AM
  4. Replies: 4
    Last Post: October 27th 2010, 05:41 AM
  5. Replies: 3
    Last Post: September 14th 2010, 02:46 PM

Search Tags


/mathhelpforum @mathhelpforum