Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By romsek

Thread: Question on differentiatialibility and continuity

  1. #1
    Super Member
    Joined
    Jul 2015
    From
    United States
    Posts
    522
    Thanks
    10

    Question on differentiatialibility and continuity

    I am reviewing all of my notes where we have a piecewise function, and I see everytime we check for differentiability, we check for continuity first. For example I will show you problem.

    I do not understand why do we check continuity first always, if the theorem holds that if it is differentiable, then it is continuous. , therefore if no continuty = no differentiation??

    Is there anyway I can check for differentation first?


    m.imgur.com/gtcEr2q
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2015
    From
    United States
    Posts
    522
    Thanks
    10

    Re: Question on differentiatialibility and continuity

    Wait, so this might make sense to me now: we check for continuity first because, if a function is differentiable it is always continous. Therefore, we must check for continuity first. And then if it is continous, then it might or might not be differentiable right? That is why we always check for contunity first.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,605
    Thanks
    2924

    Re: Question on differentiatialibility and continuity

    consider the function

    $y = \begin{cases}x-1 &x \leq 0 \\ x+1 & 0 < x\end{cases}$

    $\left. \dfrac {dy}{dx}\right|_{x=0}$ certainly seems like it should just be 1 but because of the discontinuity at $x=0$ the derivative doesn't exist there.
    Thanks from math951
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jul 2015
    From
    United States
    Posts
    522
    Thanks
    10

    Re: Question on differentiatialibility and continuity

    so always check for continuity first right? Atleast at this point? we have not learned that notation dy/dx yet.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,605
    Thanks
    2924

    Re: Question on differentiatialibility and continuity

    Quote Originally Posted by math951 View Post
    so always check for continuity first right? Atleast at this point? we have not learned that notation dy/dx yet.
    yes, you should verify a function is continuous at the point you are trying to find the derivative at.

    But just because it is discontinuous at one point doesn't mean it's not differentiable at another. It just has to be continuous at any point where a derivative exists.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuity Question
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Feb 3rd 2010, 04:58 AM
  2. continuity question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 14th 2009, 11:38 PM
  3. Continuity question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jul 3rd 2009, 10:10 AM
  4. Continuity Question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Jun 6th 2009, 09:09 PM
  5. Continuity Question
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: Feb 10th 2009, 08:56 AM

Search Tags


/mathhelpforum @mathhelpforum