Results 1 to 2 of 2

Math Help - Intermediate Value Theorem

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    51

    Intermediate Value Theorem

    im supposed to use the IVT to prove that the equation
    g(x)= 1+x + \frac{x^2}{2}+....+\frac{x^{n-1}}{n-1}+\frac{x^n}{n} has at least one real solution. where n is and odd positive integer and g(x)=0.

    im not sure if when n=3 the equation looks like g(x)=1+x+\frac{x^2}{2} + \frac{x^2}{2} + \frac{x^3}{3}

    or
    g(x)=1+x+\frac{x^2}{2}+\frac{x^3}{3}

    if its the second equation then i know that the intervals are [-2,-1] because g(-1)>g(-2)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by iLikeMaths View Post
    im supposed to use the IVT to prove that the equation
    g(x)= 1+x + \frac{x^2}{2}+....+\frac{x^{n-1}}{n-1}+\frac{x^n}{n} has at least one real solution. where n is and odd positive integer and g(x)=0.

    im not sure if when n=3 the equation looks like g(x)=1+x+\frac{x^2}{2} + \frac{x^2}{2} + \frac{x^3}{3}

    or
    g(x)=1+x+\frac{x^2}{2}+\frac{x^3}{3}

    if its the second equation then i know that the intervals are [-2,-1] because g(-1)>g(-2)
    in general any polynomial f(x) of odd degree and with real coefficients has a real root. you want to prove it using IVT:

    see that, depending on the sign of the leading coefficient of f, we have \lim_{x\to{+ \infty}}f(x)=\pm \infty and \lim_{x\to{-\infty}} f(x)=\mp \infty. so for x \gg 0: \ f(x)f(-x) < 0. now apply IVT.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intermediate Value Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 26th 2011, 01:43 PM
  2. Intermediate value theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 30th 2009, 01:10 PM
  3. Intermediate Value Theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2009, 08:49 AM
  4. Intermediate Value Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 22nd 2008, 12:33 PM
  5. intermediate value theorem/rolle's theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 8th 2007, 01:55 PM

Search Tags


/mathhelpforum @mathhelpforum