Results 1 to 4 of 4

Math Help - What value\s of c is (are) predicted by the Mean Value Theorem for f (x) = (x − 2)^3

  1. #1
    Junior Member bijosn's Avatar
    Joined
    Feb 2011
    Posts
    33

    What value\s of c is (are) predicted by the Mean Value Theorem for f (x) = (x − 2)^3

    What value(s) of c is (are) predicted by the Mean Value Theorem for f (x) = (x − 2)^3 on the interval [0, 2]?

    this is my attempt but its wrong I think

    \frac{(x-2)^4}{4}\big|_0^2
    = 0 - \frac{16}{4}
     = -4

     f(c)(b-a) = -4
     (c -2)^3(2 -0) = -4
     (c -2)^3 = -2
     (c -2) = (-2)^{\frac{1}{3}}
     c = (-2)^{\frac{1}{3}} + 2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by bijosn View Post
    What value(s) of c is (are) predicted by the Mean Value Theorem for f (x) = (x − 2)^3 on the interval [0, 2]?

    this is my attempt but its wrong I think

    \frac{(x-2)^4}{4}\big|_0^2
    = 0 - \frac{16}{4}
     = -4

     f(c)(b-a) = -4
     (c -2)^3(2 -0) = -4
     (c -2)^3 = -2
     (c -2) = (-2)^{\frac{1}{3}}
     c = (-2)^{\frac{1}{3}} + 2
    I think you may be remembering the formula wrong. Remember that it's \displaystyle f'(c)=\frac{f(b)-f(a)}{b-a}...in our case f'(c)=3(c-2)^2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member bijosn's Avatar
    Joined
    Feb 2011
    Posts
    33
    thanks, I am using the mean value theorem formula as it is in the study guide
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,427
    Thanks
    1857
    Then go back and read your study guide again! As Drexel28 said, it is f'(x)= \frac{f(b)- f(a)}{b- a}, NOT " f(x)= \frac{f(b)- f(a)}{b- a}" that you are using.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solve y ′′ − 3 y ′ − 4 y = −3 x+5
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: June 3rd 2010, 12:50 AM
  2. Graphing predicted values for generalized linear models
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 19th 2010, 12:58 PM
  3. Replies: 7
    Last Post: November 7th 2009, 05:05 AM
  4. Find gcd of 7^(4n+3) − 4^(10n+3) + 11^(10n+2)
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: September 15th 2009, 05:35 AM
  5. Replies: 8
    Last Post: April 19th 2009, 03:41 PM

Search Tags


/mathhelpforum @mathhelpforum