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Math Help - points of sruface closest to origin.

  1. #1
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    points of sruface closest to origin.

    Problem :
    Find the points on the surface xy^2z^3=2 that are closest to the origin.

    I solved it for z:
     z=\sqrt[3]{\frac{2}{xy^2}}.
    and I said:
    f(x,y)=\sqrt[3]{\frac{2}{xy^2}}
    I stopped here.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    For the solution using Lagrange multipliers see the attachment

    check my arithmetic
    Attached Thumbnails Attached Thumbnails points of sruface closest to origin.-lagrange2.jpg  
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by TWiX View Post
    Problem :
    Find the points on the surface xy^2z^3=2 that are closest to the origin.

    I solved it for z:
     z=\sqrt[3]{\frac{2}{xy^2}}.
    and I said:
    f(x,y)=\sqrt[3]{\frac{2}{xy^2}}
    I stopped here.
    The square distance:

    D^2=x^2+y^2+z^2

    so:

    D^2=x^2+\frac{2}{xz^3}+z^2

    Which leaves you with the unconstrained minimisation of a function of two variables.

    CB
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