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Math Help - Parametrization Plane Problem

  1. #1
    Del
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    Parametrization Plane Problem

    Find the maximum height above the -plane of a point on
    .

    ( x , y , z )

    I found z to be 4. Again, this is trivial. How can I find x and y for this point? Please help!
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  2. #2
    Flow Master
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    Quote Originally Posted by Del View Post
    Find the maximum height above the -plane of a point on
    .

    ( x , y , z )

    I found z to be 4. Again, this is trivial. How can I find x and y for this point? Please help!
    Clearly the maximum height above the xy-plane occurs when t(4 - t) has its maximum value.

    Consider the parabola f(t) = t(4 - t). Not hard to see that it has a maximum turning point at t = 2.

    So the maximum height is 4 and occurs at the point given by r(2) .....
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