Results 1 to 3 of 3

Math Help - Find the stationary points.

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    8

    Find the stationary points.

    Find the stationary points of this function f(x)=x^3 - 6xy + 3y^2

    Can someone please help me with calculus problem? (detailed please)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,653
    Thanks
    1478
    Your function is \displaystyle f(x,y) = x^3 - 6xy + 3y^2.

    The gradient vector is \displaystyle \nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right) and the critical points occur when \displaystyle \nabla f = \mathbf{0}.


    \displaystyle \nabla f = \left(3x^2 - 6y, -6x + 6y\right) = \mathbf{0}.


    So \displaystyle 3x^2 - 6y = 0 and \displaystyle -6x + 6y = 0.

    From the second equation, \displaystyle x = y .

    Substituting into the first gives \displaystyle 3x^2 - 6x = 0

    \displaystyle 3x(x - 2) = 0

    \displaystyle x = 0, x = 2.


    Therefore, the critical points are \displaystyle (x, y) = (0, 0) and \displaystyle (x, y) = (2, 2).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2010
    Posts
    8
    Thank you so much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Stationary points - find horizontal line
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 8th 2012, 05:29 AM
  2. Find x values of stationary points
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 27th 2011, 02:28 AM
  3. find stationary points
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: February 22nd 2010, 03:01 PM
  4. "Find all 'stationary points'.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 3rd 2009, 09:06 AM
  5. Replies: 4
    Last Post: November 3rd 2007, 01:52 PM

Search Tags


/mathhelpforum @mathhelpforum