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Math Help - closest point mmn14 4a

  1. #1
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    closest point mmn14 4a

    on the surface x^2y^2z^2=1
    find a point on this plane where it is the closest to (0,0,0)

    i know we should find a function f(x,y) which is the distance between the point on the suface oand (0,0,0)

    how to find this f(x,y)

    ?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by transgalactic View Post
    on the surface x^2y^2z^2=1
    find a point on this plane where it is the closest to (0,0,0)

    i know we should find a function f(x,y) which is the distance between the point on the suface oand (0,0,0)

    how to find this f(x,y)

    ?
    Minimise

    d^2=x^2+y^2+z^2

    subject to

    x^2y^2z^2=1

    Lagrange multiplier problem, now show us what you have done or explain where you are having difficulties.

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Minimise

    d^2=x^2+y^2+z^2

    subject to

    x^2y^2z^2=1

    Lagrange multiplier problem, now show us what you have done or explain where you are having difficulties.

    CB
    ok
    z=g(x,y)=\sqrt{\frac{1}{x^2y^2}}


    d^2=x^2+y^2+z^2
    f(x,y)=d^2=x^2+y^2+(\sqrt{\frac{1}{x^2y^2}})^2

    can i use the d^2 formula
    and find its minimal points instead of the "d" formula
    ?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by transgalactic View Post
    ok
    z=g(x,y)=\sqrt{\frac{1}{x^2y^2}}


    d^2=x^2+y^2+z^2
    f(x,y)=d^2=x^2+y^2+(\sqrt{\frac{1}{x^2y^2}})^2

    can i use the d^2 formula
    and find its minimal points instead of the "d" formula
    ?
    d is a minimum if and only if d^2 is a minimum when d is a distance.

    CB
    Last edited by CaptainBlack; June 8th 2011 at 07:30 PM.
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