Results 1 to 3 of 3

Math Help - Using Mean Value Theorem to show solutions ?

  1. #1
    Member
    Joined
    Apr 2009
    Posts
    108

    Using Mean Value Theorem to show solutions ?

    Suppose xe^-x=(x-1)^2

    Use the Mean value theorem to show that this equation has exactly two solutions...

    Well I know the mean value theorem is

    f'(c)= f(b)-f(a)/b-a

    this is the f'(x)

    how do we use the first derivative to show a solutions ??

    Once again sorry guys- I'm just first year maths student

    I'm just doing past papers and like they never taught us how to use mean value theorem but its in the exam ???????????

    The notes only go in brief ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Khonics89 View Post
    Suppose xe^-x=(x-1)^2

    Use the Mean value theorem to show that this equation has exactly two solutions...

    Well I know the mean value theorem is

    f'(c)= f(b)-f(a)/b-a

    this is the f'(x)

    how do we use the first derivative to show a solutions ??

    Once again sorry guys- I'm just first year maths student

    I'm just doing past papers and like they never taught us how to use mean value theorem but its in the exam ???????????

    The notes only go in brief ?
    Consider:

    f(x)=xe^{-x}-(x-1)^2

     <br />
f'(x)=(1-x)(e^{-x}+2)<br />

    So f'(x)<0 when x>1, and f'(x)>0 when x<1, so we have f(x) is decreasing when x>1 and increasing when x<0.

    Now f(1)>0 and f(0)=-1, so by the intermediate value theorem as there is a root of f(x)=0 between 0 and 1, and there can be no other zeros less than 1 as f(x) is increasing there.

    Same argument applies to x>1.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    I am not making the connection to the mean value theorem here...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Is it possible to show this equation has no solutions
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: December 29th 2011, 02:40 AM
  2. Show that a^2 -1 = 0 mod p has only 2 solutions
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 23rd 2011, 08:14 PM
  3. Show that x^2*e^|x|=2 has two solutions
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 13th 2010, 07:12 AM
  4. Replies: 5
    Last Post: May 21st 2009, 12:31 PM
  5. Show solutions are global
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 4th 2009, 12:06 PM

Search Tags


/mathhelpforum @mathhelpforum