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Math Help - Help with Lagrange multiplier Problems

  1. #1
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    Help with Lagrange multiplier Problems

    Can someone help me on the following Lagrange multiplier problems:


    1.) Find the points of the parabola y = (x-1)^2 that are closest to the origin.

    2.) Find the first-quadrant point of the curve xy=24 that is closest to the point (1,4)

    3.) Find teh points on teh sphere with center (1,2,3) and radius 6 that are closest to and farthest from the origin
    Last edited by mr fantastic; October 16th 2009 at 09:13 PM.
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  2. #2
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    Quote Originally Posted by messianic View Post
    Can someone help me on the following Lagrange multiplier problems:


    1.) Find the points of the parabola y = (x-1)^2 that are closest to the origin.

    2.) Find the first-quadrant point of the curve xy=24 that is closest to the point (1,4)

    3.) Find teh points on teh sphere with center (1,2,3) and radius 6 that are closest to and farthest from the origin
    1. Find the point that minimises D = x^2 + y^2 subject to the constraint y = (x - 1)^2.

    2. Find the point that minimises D = (x-1)^2 + (y-4)^2 subject to the constraint xy = 24.

    3. Find the points that minimise and maximise D = x^2 + y^2 + z^2 subject to the constraint (x-1)^2 + (y-2)^2 + (z-3)^2 = 6^2.

    If you need more help please post all your working and state where you get stuck.
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