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Math Help - Tangent planes

  1. #1
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    Tangent planes

    Hi guys,

    I have a problem: for the equation f(x,y)=e^xln(y), how do I determine if the surface z=f(x,y) has any horizontal tangent planes?

    The thing that's tripping me up is the "horizontal" part.

    Any help would be most appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by HFLER View Post
    Hi guys,

    I have a problem: for the equation f(x,y)=e^xln(y), how do I determine if the surface z=f(x,y) has any horizontal tangent planes?

    The thing that's tripping me up is the "horizontal" part.

    Any help would be most appreciated. Thanks!
    If the tangent plane is horizontal to the surface then the normal to the plane will be \vec{n} = \pm k.
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  3. #3
    MHF Contributor matheagle's Avatar
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    All the directional derivatives must be zero.
    Hence all partial derivatives must be zero.

    BUT f_x=e^x\ln y and f_y={e^x\over y} are never zero.

    We can let y=1, but f_y={e^x\over y} is never zero, I should say.
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