Results 1 to 2 of 2

Math Help - Third Derivitive of Decreasing Function

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    14

    Third Derivitive of Decreasing Function

    Hi guys, im stuck on a problem, this is it:
    ------

    Let f(x) = - u''(x)/u'(x)
    Show that if f(x) is decreasing then u'''(x) is greater than 0.

    ----
    Thanks Guys, ive been at it for a while and cant get it
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,339
    Thanks
    21
    Quote Originally Posted by furnis1 View Post
    Hi guys, im stuck on a problem, this is it:
    ------

    Let f(x) = - u''(x)/u'(x)
    Show that if f(x) is decreasing then u'''(x) is greater than 0.

    ----
    Thanks Guys, ive been at it for a while and cant get it
    If f = - \frac{u''}{u'} then f' = - \left( \frac{u' u''' - u''^2}{u'^2} \right). If f' < 0 then  - \left( \frac{u' u''' - u''^2}{u'^2} \right) < 0 so  \left( \frac{u' u''' - u''^2}{u'^2} \right) > 0 so u' u''' - u''^2 > 0 giving u' u''' > u''^2 so u' u''' > 0 . You need the product. It is possible to come up with a function that  u' > 0\;\;\text{and}\;\;\; u'''<0.

    Case in point u ' = e^{-x^2} so f = -2x\;\;\Rightarrow\;\; f' = -2 < 0 yet u''' = (4x^2-2)e^{-x^2} which is not always positive for all x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivitive of this function...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 22nd 2011, 09:40 PM
  2. Derivitive of a Sqrt of a rational function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 2nd 2010, 06:20 PM
  3. time derivitive - inventory model function
    Posted in the Business Math Forum
    Replies: 0
    Last Post: November 25th 2009, 09:24 PM
  4. decreasing function
    Posted in the Math Software Forum
    Replies: 0
    Last Post: March 19th 2008, 01:59 AM
  5. Derivitive and function help.
    Posted in the Calculus Forum
    Replies: 8
    Last Post: September 29th 2006, 05:33 PM

Search Tags


/mathhelpforum @mathhelpforum