Results 1 to 2 of 2

Math Help - global max an global min

  1. #1
    Junior Member
    Joined
    Aug 2008
    Posts
    44

    global max an global min




    my try on problem2 was take the partial devaritive eaqual to zero, get the C.P. then take the boundary point (3,2) , to find the max and min. it that right?



    also, how to do problem#4?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,689
    Thanks
    617
    Hello, yzc717;230977!

    I would use Lagrange Multipliers on #4 . . .


    4. Find the points on the curve of intersection of the surfaces: . \begin{array}{c}x^2 - xy + y^2 - z^2 \:=\:1 \\ x^2+y^2+1 \end{array}
    in \Re^2 that are closest to the origin.

    We want to minimize: . d(x,y,z) \:=\:x^2+y^2+z^2
    . with the constraints: . x^2-xy+y^2-z^2 -1\:=\:0\:\text{ and }\;x^2+y^2-1\:=\:0


    We have: . f(x,y,z,\lambda,\mu) \;=\;x^2+y^2+z^2 + \lambda(x^2-xy+y^2-z^2-1) + \mu(x^2+y^2-1)


    Take partial derivatives and equate to zero . . .

    . . f_x \;=\;2x + \lambda(2x-y) + \mu(2x) \;=\;0

    . . f_y \;=\;2y + \lambda(-x+2y) + \mu(2y) \;=\;0

    . . f_z \;=\;2z + \lambda(-2z) \;=\;0

    . . f_{\lambda} \;=\;x^2-xy+y^2-z^2-1\;=\;0

    . . f_{\mu} \;=\;x^2+y^2 -1\;=\;0


    Then solve the system for: . \lambda, \mu, x, y, z.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 15th 2010, 02:43 AM
  2. Global Extrema Help
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 29th 2009, 10:14 AM
  3. Help with local max/min and global max/min
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 17th 2009, 01:28 PM
  4. Global Extrema
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 15th 2009, 03:06 AM
  5. Global max/min.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 28th 2008, 12:43 PM

Search Tags


/mathhelpforum @mathhelpforum