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Lagrange multipliers

  1. Sep 25, 2005 #1
    Find the shortest and longest distance from the origin to the curve
    [tex]x^2 + xy + y^2=16[/tex] and give a geometric interpretation...the hint given is to find the maximum of [tex]x^2+y^2[/tex]

    i am not sure what to do for this problem

  2. jcsd
  3. Sep 25, 2005 #2
    Are you sure you need Lagrange Multipliers for this?
  4. Sep 25, 2005 #3
    it says for the hint to use the method of lagrange multipliers to find the maximum of [tex]x^2 + y^2[/tex] but i am not sure how to do it using any method, so any help is appreciated.
  5. Sep 25, 2005 #4
    Solve for y. use rate of change respect to the distance.
    that is the "cal 1 method"

    the path equation is constraint i think. apply Lagrange Multipliers on the distance formula
    Last edited: Sep 25, 2005
  6. Sep 25, 2005 #5
    solve for y in what though. in the question it says [tex]x^2+y^2[/tex] this isnt even an equation though.
    im sorry i still dont get it
  7. Sep 25, 2005 #6
    you can solve for y in tern of x
    and then using the distance formula D = (y^2+x^2)^0.5
    sub the y equation into the distance formula
    take the first derivative
    fine 0s
    test it

    that is cal 1 method, it requires a lot of work

    [tex]x^2+y^2[/tex] looks really similar to the distance formula
    [tex]D^2 = x^2 + y^2[/tex]

    you can set [tex] D = f(x)[/tex] or [tex] D^2 = f(x)[/tex] and find the del of it, since the square doesnt where the extreme occurs, therefore the text tells you to fine the max of [tex]x^2+y^2[/tex]
    Last edited: Sep 25, 2005
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