Results 1 to 2 of 2

Math Help - Application of derivatives?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Application of derivatives?

    Given that \sum_{k = 0}^{n - 1} a_{k} = 0 where a_{k} \in \mathbb{R}\ \forall\ k = 0, 1, 2,\mbox{....},(n - 1).

    Show that a_{i_{0}}\cdot n\cdot x^{n - 1} + a_{i_{1}}\cdot (n - 1)\cdot x^{n - 2} + ... + a_{i_{n - 2}}\cdot 2x + a_{i_{n - 1}} = 0 has at least one real root in (-3, 3) for any permutation (a_{i_{0}}, a_{i_{1}},\mbox{.....},a_{i_{n - 1}}\ \mbox{of}\ a_0,a_1,\mbox{.....},a_{n - 1}).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by fardeen_gen View Post
    Given that \sum_{k = 0}^{n - 1} a_{k} = 0 where a_{k} \in \mathbb{R}\ \forall\ k = 0, 1, 2,\mbox{....},(n - 1).

    Show that a_{i_{0}}\cdot n\cdot x^{n - 1} + a_{i_{1}}\cdot (n - 1)\cdot x^{n - 2} + ... + a_{i_{n - 2}}\cdot 2x + a_{i_{n - 1}} = 0 has at least one real root in (-3, 3) for any permutation (a_{i_{0}}, a_{i_{1}},\mbox{.....},a_{i_{n - 1}}\ \mbox{of}\ a_0,a_1,\mbox{.....},a_{n - 1}).
    trivial! let f(x)=a_{i_0}x^n + a_{i_1}x^{n-1} + \cdots + a_{i_{n-1}}x. then f(0)=f(1)=0 and thus by Rolle's theorem f'(x)=0 has a root in the interval (0,1).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Application of Derivatives-is this correct
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 12th 2010, 03:32 AM
  2. Application of Derivatives ( Optimization )
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 12th 2010, 06:25 AM
  3. Application of Derivatives
    Posted in the Math Challenge Problems Forum
    Replies: 2
    Last Post: June 18th 2009, 05:16 PM
  4. Application of derivatives
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 15th 2008, 04:52 PM
  5. Application of derivatives
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 29th 2007, 07:32 AM

Search Tags


/mathhelpforum @mathhelpforum