Results 1 to 5 of 5

Math Help - Increasing interval and decreasing interval

  1. #1
    Member
    Joined
    Jul 2005
    Posts
    187

    Increasing interval and decreasing interval

    I have got a complex function y=(x^2-4*x-1)/(2*x+1) and I have to show the increasing and decreasing intervals.
    How to show it when y'=(2*x^2+2*x-2)/(2*x+1)^2 but I am not able to find zero points and therefore it is impossible to find the increasing and decreasing intervals.
    Any advice ?
    Attached Thumbnails Attached Thumbnails Increasing interval and decreasing interval-increase.jpg  
    Last edited by totalnewbie; February 24th 2006 at 07:28 AM.
    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 totalnewbie
    I have got a complex function y=(x^2-4*x-1)/(2*x+1) and I have to show the increasing and decreasing intervals.
    How to show it when y'=(2*x^2+2*x-2)/(2*x+1)^2 but I am not able to find zero points and therefore it is impossible to find the increasing and decreasing intervals.
    Any advice ?
    Sketch the curve:
    Attached Thumbnails Attached Thumbnails Increasing interval and decreasing interval-graph1.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2005
    Posts
    187
    This is not precise answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    The function,
    y=\frac{x^2-4x-1}{2x+1},x\not =-1/2 then,
    y'=\frac{2x^2+2x-2}{(2x+1)^2},x\not =-1/2.
    By Fermat's Principle the necessary conditions is when the derivative is zero or does not exits. Notice it does not exist at x=-1/2 but the function itself does not posses that domain. Thus, y'=0. That happens when 2x^2+2x-2=0,
    Thus,
    x^2+x-1=0
    x=\frac{-1\pm\sqrt{5}}{2}.
    Now you can use derivative test to determine whether they are maximum or minimum or neither.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by totalnewbie
    This is not precise answer.
    No its not, its a hint.

    You have two points at which the derivative is zero and one point at
    which it goes to infinity which is between the zeros of the derivative.

    It is increasing from -infinity to the first turning point decreasing
    from there to the singularity, then decreasing from the singularity
    to the next turning point and increasing from there out to +infinity.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: October 20th 2009, 01:12 PM
  2. Replies: 5
    Last Post: December 22nd 2008, 04:10 PM
  3. Replies: 1
    Last Post: November 28th 2008, 09:16 AM
  4. Replies: 4
    Last Post: November 14th 2008, 04:48 PM
  5. increasing on interval?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 24th 2008, 11:16 PM

Search Tags


/mathhelpforum @mathhelpforum