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    Lagrange Multipliers

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    The plane, 4*x - 3*y + 8*z = 5, intersects the cone, z^2 = x^2 + y^2, in an ellipse.

    1. Graph the cone, the plane and the ellipse

    2. Using lagrange multipliers find the highest and lowest points on the ellipse.

    Please show grophs, equation of the ellipse and all work.

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    Solution Preview

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    The solution is attached below (next to the paperclip icon) in two formats. one is in Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

    The Cone-Plane system looks like:

    And the ellipse is clearly visible from a top view:

    We are interested at the points on the ellipse that have the minimal and maximal ...

    Solution Summary

    The highest and lowest points of an ellipse that results from intersection of a plane with a cone are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.