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Math Help - Partial Derivitives

  1. #1
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    Partial Derivitives

    Find direction of normal and the equation of the tangent plane at the point.

    z=sqrt(4-x^2-y^2)

    at (1,1,sqrt(2))
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    Last edited by heatly; March 5th 2011 at 12:54 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Use the well known result:

    \vec{v}=(f_x(P_0),f_y(P_0),-1)

    is an orthogonal vector to the tangent plane for the surface S\equiv z=f(x,y) at P_0(x_0,y_0,z_0)\in S.
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  3. #3
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    I prefer to think of such a surface as being a level surface for g(x,y,z)= f(x,y)- z= 0 and using the fact that the gradient, \nabla g= f_x\vec{i}+ f_y\vec{j}- \vec{k}, is normal to a level surface. Of course, that gives exactly the same thing FernandoRevilla is saying.
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