Results 1 to 2 of 2

Math Help - Rolle's Theorem

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    12

    Rolle's Theorem

    This is the last part of a problem that I'm working through. The problem is on Rolle's theorem.

    Using Rolles Theorem prove that for any real number λ: the function f(x) = x^3 - (3/2)x^2 + λ never has two distinct zeros in [0,1].

    So I was thinking about ways I could do this: but when I calculated f(0) = λ, wheras f(1) = λ-1/2, but to use Rolle's theorem isnt f(a) = f(b) on the interval [a,b]?? This has got me a little confused.
    Anyway I put that aside to try another way:
    I thought perhaps I should assume for contradiction that I should assume there are two distinct zeros at c1 and c2. So f'(c1 = f'(c2) = 0. But then using Rolles Theorem there is a root of f between c1 and c2. But now I don't know where to go with this next! Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,238
    Thanks
    1795
    Quote Originally Posted by reeha View Post
    This is the last part of a problem that I'm working through. The problem is on Rolle's theorem.

    Using Rolles Theorem prove that for any real number λ: the function f(x) = x^3 - (3/2)x^2 + λ never has two distinct zeros in [0,1].

    So I was thinking about ways I could do this: but when I calculated f(0) = λ, wheras f(1) = λ-1/2, but to use Rolle's theorem isnt f(a) = f(b) on the interval [a,b]?? This has got me a little confused.
    Anyway I put that aside to try another way:
    I thought perhaps I should assume for contradiction that I should assume there are two distinct zeros at c1 and c2. So f'(c1 = f'(c2) = 0. But then using Rolles Theorem there is a root of f between c1 and c2. But now I don't know where to go with this next! Please help!
    Yes, that second method is the way to go. But you are going the wrong way!
    Rolles theorem does not say that if f'(c1)= f'(c2)= 0, then there is a zero of f between c1 and c2. It says the if f(c1)= f(c2)= 0, then there is a zero of f' between c1 and c2. Since f(x)= x^3 - (3/2)x^2 + \lambda, f'(x)= 3x^2- 3x= 3x(x- 1). The zeros of that are x= 0 and x= 1. There is no 0 between such c1 and c2!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rolle's Theorem
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 19th 2010, 08:31 PM
  2. rolle's theorem
    Posted in the Calculus Forum
    Replies: 9
    Last Post: December 21st 2009, 07:04 PM
  3. Rolle's Theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 26th 2009, 03:56 PM
  4. intermediate value theorem/rolle's theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 8th 2007, 02:55 PM
  5. Rolle's Theorem Help :D
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 18th 2007, 10:38 AM

Search Tags


/mathhelpforum @mathhelpforum