Results 1 to 2 of 2

Math Help - Calculus Max and Min

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    71

    Calculus Max and Min

    Consider the function f(x)=sin(x)+(1/4)*sin(2x) on the interval [0,2pi].

    Find numbers a, b and c so that a < b < c and f(x) is concave in one direction

    on each of the intervals (0,a),(a,b),(b,c) and (c,2pi).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Velvet Love View Post
    Consider the function f(x)=sin(x)+(1/4)*sin(2x) on the interval [0,2pi].

    Find numbers a, b and c so that a < b < c and f(x) is concave in one direction

    on each of the intervals (0,a),(a,b),(b,c) and (c,2pi).
    f'(x) = \cos{x} + \frac{1}{2}\cos(2x)

    f''(x) = -\sin{x} - \sin(2x) = -\sin{x} - 2\sin{x}\cos{x} = 0

    -\sin{x}(1 + 2\cos{x}) = 0

    set each factor equal to 0 and solve for x , then determine the concavity of each interval between the critical values.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 13th 2011, 09:11 PM
  2. Replies: 2
    Last Post: June 25th 2010, 10:41 PM
  3. Replies: 1
    Last Post: February 11th 2010, 07:09 AM
  4. Calculus III But doesn't require Calculus :)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 19th 2009, 04:23 PM
  5. Replies: 1
    Last Post: June 23rd 2008, 09:17 AM

Search Tags


/mathhelpforum @mathhelpforum