Results 1 to 9 of 9

Thread: Differentiable function problem

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    israel
    Posts
    70

    Differentiable function problem

    $\displaystyle f $ is a differentiable function at $\displaystyle x=1$.prove that if $\displaystyle \lim_{h\rightarrow0}\frac{f(1+h)}{h}=1 $
    so, $\displaystyle f(1)=0 $ & $\displaystyle f'(1)=1 $
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,797
    Thanks
    2828
    Awards
    1

    Re: Differentiable function problem

    Quote Originally Posted by orir View Post
    $\displaystyle f $ is a differentiable function at $\displaystyle x=1$.prove that if $\displaystyle \lim_{h\rightarrow0}\frac{f(1+h)}{h}=1 $
    so, $\displaystyle f(1)=0 $ & $\displaystyle f'(1)=1 $

    If $\displaystyle f(1)\ne 0$ is it possible for $\displaystyle {\lim _{h \to 0}}\frac{{f(1)}}{h}$ to exist? Why or why not?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2013
    From
    israel
    Posts
    70

    Re: Differentiable function problem

    i actually don't know what to answear to that.. :S
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,797
    Thanks
    2828
    Awards
    1

    Re: Differentiable function problem

    Quote Originally Posted by orir View Post
    i actually don't know what to answear to that.. :S

    Why don't you know that? It happens to be the key to this whole question.

    What is $\displaystyle {\lim _{h \to 0}}~\frac{3}{h}=~?$ Can you work that out?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2013
    From
    israel
    Posts
    70

    Re: Differentiable function problem

    this lim doesn't exist... so? how this helps me?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,797
    Thanks
    2828
    Awards
    1

    Re: Differentiable function problem

    Quote Originally Posted by orir View Post
    this lim doesn't exist... so? how this helps me?
    You are given that both
    $\displaystyle {\lim _{h \to 0}}\frac{{f(1 + h)}}{h}\quad \& \quad {\lim _{h \to 0}}\frac{{f(1 + h) - f(1)}}{h}$ EXIST.

    Now doesn't that imply that $\displaystyle {\lim _{h \to 0}}\frac{{f(1)}}{h}$ must also exists?

    If so, what does that tell you about $\displaystyle f(1)~?$ And why?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Mar 2013
    From
    israel
    Posts
    70

    Re: Differentiable function problem

    i guess it tells me that $\displaystyle f(1)=0 $...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,797
    Thanks
    2828
    Awards
    1

    Re: Differentiable function problem

    Quote Originally Posted by orir View Post
    i guess it tells me that $\displaystyle f(1)=0 $...

    Correct! So what is $\displaystyle f'(1)~?$
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Mar 2013
    From
    israel
    Posts
    70

    Re: Differentiable function problem

    1! thank you...
    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. Is this function differentiable?
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Sep 8th 2010, 05:46 AM
  3. differentiable function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 20th 2010, 04:25 AM
  4. Replies: 1
    Last Post: Mar 7th 2010, 09:20 PM
  5. Differentiable function
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Oct 12th 2009, 06:01 PM

Search Tags


/mathhelpforum @mathhelpforum