Results 1 to 2 of 2

Math Help - Interemediate Value Rule of Derivatives

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    178

    Interemediate Value Rule of Derivatives

    If y=f(x) is continuous on [a,b], and N is a number between f(a) and f(b), then there is at least 1 c ∈ [a,b] such that f(c) = N.

    That's actually the normal value. They're fundamentally the same.
    So according to this, if I get it,
    if y= |x| is differentiable at [-1, 1] then everything between the two is differentiable. But 0 isn't differentiable.
    Something about my logic, if it's even worth calling that, is seriously weird.

    Woulds someone explain my prob? Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Truthbetold View Post
    If y=f(x) is continuous on [a,b], and N is a number between f(a) and f(b), then there is at least 1 c ∈ [a,b] such that f(c) = N.

    That's actually the normal value. They're fundamentally the same.
    So according to this, if I get it,
    if y= |x| is differentiable at [-1, 1] then everything between the two is differentiable. But 0 isn't differentiable.
    Something about my logic, if it's even worth calling that, is seriously weird.

    Woulds someone explain my prob? Thank you!
    A function is said to have the intermediate value property on an interval I (it can be any interval, open, closed, infinite, ... ) iff for any a<b in I we have that if N is between f(a) and f(b) in value then there exists c in [a,b] so that f(c) = N.

    Now if f is differenciable on an open interval I then f' has the intermediate value property on I. That is the theorem. What you wrote does not satisfy the conditions of this theorem, which is why it is not working.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] L'Hopital's Rule and Derivatives
    Posted in the Calculus Forum
    Replies: 17
    Last Post: July 31st 2010, 03:00 PM
  2. Derivatives Quotient Rule
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 17th 2010, 01:34 PM
  3. Derivatives - product rule + chain rule
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 19th 2009, 03:26 PM
  4. Power Rule for derivatives
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 18th 2008, 05:17 PM
  5. Power Rule Derivatives
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 2nd 2006, 10:42 AM

Search Tags


/mathhelpforum @mathhelpforum