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Homework Help: Lagrange Multipliers - basic which value?

  1. Apr 7, 2008 #1
    (1) [tex]f(x,y,z)=x+2y[/tex]
    (2) [tex]x+y+z=1[/tex]
    (3) [tex]y^2+z^2=4[/tex]

    [tex]1=\lambda[/tex]
    [tex]2=\lambda+2y\mu[/tex]
    [tex]0=\lambda+2z\mu[/tex]

    [tex]u=\frac{1}{2y}[/tex]
    [tex]y=\pm\sqrt2 \ \ \ z=\pm\sqrt2[/tex]

    Plugging into equation 2 to solve for x.

    How do I know to use either [tex]y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2[/tex] ... similarly with my values for z.

    edit: NVM, I'm an idiot :p I overlooked a step, which told me that [tex]z=-y[/tex]

    ... too late to delete?
     
    Last edited: Apr 7, 2008
  2. jcsd
  3. Apr 7, 2008 #2
    see the geometry (It's a plane)

    f(x,y) = ..

    I was thinking about f_xx*f_yy - (f_xy)^2 thing,
    but my teacher says it's very hard to *identify* max min in Lagrange; should use geometry
     
    Last edited: Apr 7, 2008
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