Results 1 to 2 of 2

Math Help - Differentiation

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Lancaster
    Posts
    20

    Differentiation

    f(x) = (x) / (1 + |x|)
    Show from the definition that f: R -> R is differentiable at 0 and find the value of f'(0)

    I have been trying to do it from first principles but keep getting no where.

    Any help would be appreciated

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Differentiation

    Note that

    f(0)=0



    Using the limit definition. Taking the limit from the right gives

    f'(0)=\lim_{h \to 0^+}\frac{\frac{h}{1+h}-0}{h}=\lim_{h \to 0^+}\frac{1}{1+h}=1

    Taking the limit from the left

    f'(0)=\lim_{h \to 0^-}\frac{\frac{h}{1-h}-0}{h}=\lim_{h \to 0^-}\frac{1}{1-h}=1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differentiation
    Posted in the Calculus Forum
    Replies: 7
    Last Post: July 23rd 2011, 10:38 AM
  2. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  3. Differentiation and partial differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 30th 2010, 10:16 PM
  4. Differentiation and Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 6th 2009, 04:07 AM
  5. Differentiation! Please help!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 28th 2008, 06:16 PM

Search Tags


/mathhelpforum @mathhelpforum