Results 1 to 3 of 3

Math Help - Showing there is no anti-derivative for piecewise function?

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    65

    Showing there is no anti-derivative for piecewise function?

    I am having difficulty with this question. I think the problem im having is showing how the antiderivative does not exist ( for example what are the requirements needed for it not to exist). The second problem I have is that im not sure how to solve these type of questions when given piecewise functions.

    The question states:" show that the function f(x)=x for x less than or equal to 0 and f(x)=1 for greater than 0 has no antiderivative on R. Hint find a potential antiderivative F of f and show that F has no derivative at 0."

    Any help would be greatly appreciated
    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    This problem is very similar to the other thread that I just answered.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,055
    Thanks
    1684
    Quote Originally Posted by Solid8Snake View Post
    I am having difficulty with this question. I think the problem im having is showing how the antiderivative does not exist ( for example what are the requirements needed for it not to exist). The second problem I have is that im not sure how to solve these type of questions when given piecewise functions.

    The question states:" show that the function f(x)=x for x less than or equal to 0 and f(x)=1 for greater than 0 has no antiderivative on R. Hint find a potential antiderivative F of f and show that F has no derivative at 0."

    Any help would be greatly appreciated
    Thanks in advance!
    Looks like you just need to follow the hint! Can you find an anti-derivative for f(x)= x? Can you find an anti-derivative form f(x)= 1?
    Can you "fix" a constant of integration to fit those two together to give a purported 'anti-derivative' for this function of this problem. Now, try to differentiate that "anti-derivative".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Showing a piecewise function is one-to-one
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: February 24th 2011, 04:19 PM
  2. derivative of a piecewise function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 25th 2011, 12:56 AM
  3. Showing a piecewise function is smooth
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: March 16th 2010, 09:12 AM
  4. Derivative of a Piecewise Function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 2nd 2009, 06:23 PM
  5. derivative of a piecewise function
    Posted in the Calculus Forum
    Replies: 10
    Last Post: August 16th 2007, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum