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Math Help - Points on a surface and differentiability.

  1. #1
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    Points on a surface and differentiability.

    pls help me. I have out of idea how to get started
    Consider the surface
    Describe the set of points on the surface for which it is not possible to define the surface as the graph of a differentiable function .
    Your answer should be in the form
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    Last edited by mr fantastic; October 17th 2009 at 06:17 PM. Reason: Changed post title
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by zpwnchen View Post
    pls help me. I have out of idea how to get started

    Consider the surface
    Describe the set of points on the surface for which it is not possible to define the surface as the graph of a differentiable function .
    Your answer should be in the form
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    Differentiate implicitly to find \frac{\partial z}{\partial x} and \frac{\partial z}{\partial y} and find where they are undefined. (This will be when the denominator is 0.) Since there are no terms containing x, y, and z, the denominators for both partial derivatives will be the same. If my calculations are correct, you should get:

    g(x,y,z)=x^6+y^3\cos(y^3 z^3)=0
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  3. #3
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    I got it! thank you so much!
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