Results 1 to 3 of 3

Math Help - sketching contours

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    22

    sketching contours

    I have the function f(x,y)= 2x^3 + 3xy + 2y^3, I have found the 2 critical points for x in R and y in R.
    I believe they are (0,0) and (-1/8, 1/2)?!
    I then found that they are both saddle points which is when I doubted whether these critical points are correct.
    I then have to sketch the contours which I have attempted but am unsure if I have constructed the sketch correctly.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by linearalgebradunce View Post
    I have the function f(x,y)= 2x^3 + 3xy + 2y^3, I have found the 2 critical points for x in R and y in R.
    I believe they are (0,0) and (-1/8, 1/2)?!
    I then found that they are both saddle points which is when I doubted whether these critical points are correct.
    I then have to sketch the contours which I have attempted but am unsure if I have constructed the sketch correctly.
    The equations to solve are:

    6 x^2 + 3y = 0 \Rightarrow 2 x^2 + y = 0 .... (1)

    3x + 6 y^2 = 0 \Rightarrow x = -2 y^2 .... (2)

    Substitute (2) into (1):

    8 y^4 + y = 0 \Rightarrow y (8 y^3 + 1) = 0

    \Rightarrow y = 0, ~ - \frac{1}{2} .....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    22
    ok i have rectified my mistake and adjusted y=1/2 to y=-1/2 with corresponding x value -1/2?! so this is a maximum.
    how do i construct a sketch of the contours?!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral of Z^20 dz over different contours.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 24th 2011, 08:47 PM
  2. contours
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 9th 2010, 10:40 AM
  3. Sketching contours ellipse help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 27th 2009, 04:19 AM
  4. Sketching contours maths?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 26th 2009, 12:12 PM
  5. rectangular contours
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 29th 2007, 06:14 PM

Search Tags


/mathhelpforum @mathhelpforum