Results 1 to 3 of 3

Math Help - Mean Value/Rolle's Theorem

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    43

    Mean Value/Rolle's Theorem

    Consider the function f(x)=6x^4-7x+1 on the interval [1/2,2]. f has at least one zero in [1/2,2] (actually f(1)=0) so show that f has *exactly* on zero in the indicated interval. Hint:Use the Mean Value Theorem/Rolle's Theorem to prove the result.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by Zocken View Post
    Consider the function f(x)=6x^4-7x+1 on the interval [1/2,2]. f has at least one zero in [1/2,2] (actually f(1)=0) so show that f has *exactly* on zero in the indicated interval. Hint:Use the Mean Value Theorem/Rolle's Theorem to prove the result.
    if f had more than one zero in [1/2, 2], then by Rolle's theorem f'(x)=0 would have at least one root in [1/2, 2]. but the (real) root of f'(x)=24x^3-7=0 is x=\sqrt[3]{7/24} \notin [1/2 , 2].
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2009
    Posts
    43
    wow makes it so simple. thanks a bunch!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rolle's Theorem
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 28th 2010, 01:25 AM
  2. Rolle's Theorem
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 27th 2010, 02:59 PM
  3. Rolle's Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 28th 2009, 09:35 AM
  4. intermediate value theorem/rolle's theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 8th 2007, 01:55 PM
  5. Rolle's Theorem Help :D
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 18th 2007, 09:38 AM

Search Tags


/mathhelpforum @mathhelpforum