Results 1 to 2 of 2

Math Help - Please help: mean value theorem

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    30

    Please help: mean value theorem

    Let f(x) = x + sin2x on [0, 2(pi)] find two numbers c that satisfy the conclusion of hte Mean Value Theorem. (note there are four such numbers.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    a=0, \;\ b=2\pi

    f(x)=x+sin(2x)

    f(a)=0, \;\ f(b)=2\pi

    f'(x)=2cos(2x)+1

    f'(c)=2cos(2c)+1

    Also, f'(c)=\frac{f(b)-f(a)}{b-a}=\frac{2\pi-0}{2\pi-0}=1

    So, we have 2cos(2c)+1=1

    Solving for c we find c=\frac{(2c-1){\pi}}{4}

    When c= 1 through 4, we get:

    c=\frac{\pi}{4}, \;\ \frac{3\pi}{4}, \;\ \frac{5\pi}{4}, \;\ \frac{7\pi}{4}

    are the four points which satisfy the MVT over the given interval.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: January 10th 2011, 08:51 AM
  2. Replies: 3
    Last Post: May 14th 2010, 10:04 PM
  3. Prove Wilson's theorem by Lagrange's theorem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 10th 2010, 01:07 PM
  4. Replies: 2
    Last Post: April 3rd 2010, 04:41 PM
  5. Replies: 0
    Last Post: November 13th 2009, 05:41 AM

Search Tags


/mathhelpforum @mathhelpforum