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Homework Help: Lagrange multpliers

  1. Oct 15, 2011 #1
    Use lagrange multipliers to find max/min of
    f(x,y)=x^2+6y
    subject to
    x^2-y^2=5

    grad f =λgrad g
    2x=2xλ, λ=1
    6=-2yλ, λ=-3/y
    1=-3/y, y=-3

    x^2-(-3)^2=x^2-9=5
    x^2=14
    x=+/-√14
    two points are √14, -3 and -√14, -3
    plugging both points into f(x,y) gives me the same answer. now what?
     
  2. jcsd
  3. Oct 15, 2011 #2

    Ray Vickson

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    Science Advisor
    Homework Helper


    There are two constrained minima but no constrained maxima. Why not? Well, we can find values of x and y that together go to infinity along the curve g = 0, and when we do that we get f --> +infinity.

    RGV
     
  4. Oct 15, 2011 #3
    thank you very much
     
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