Results 1 to 2 of 2

Math Help - Rolle's Thm and the mean value thm

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    1

    Rolle's Thm and the mean value thm

    Show that cos x = x^3+x^2+4x has exactly one root in [0, 3.14.../2]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by cocoabird1985 View Post
    Show that cos x = x^3+x^2+4x has exactly one root in [0, 3.14.../2]
    Let f(x) = x^3 + x^2 + 4x - \cos x.
    Use the Intermediate Value Theorem to show that f(x) has at least one root in the interval \left[ 0, \, \frac{\pi}{2}\right].

    Now assume f(x) has two roots, a and b say, in the interval \left[ 0, \, \frac{\pi}{2}\right]. Then f(a) = f(b) = 0. Now use Rolles Theorem on the closed interval [a, b] to show that this leads to an impossibility ..... (Big Hint: Consider the turning point of y = 3x^2 + 2x + 4).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rolle's Theorem!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 21st 2010, 09:50 PM
  2. Rolle's Theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 16th 2009, 08:09 PM
  3. Rolle's Theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 28th 2009, 11:36 AM
  4. Rolle's Theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 26th 2009, 03:56 PM
  5. Mean Value/Rolle's Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 28th 2009, 05:24 PM

Search Tags


/mathhelpforum @mathhelpforum