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Partial Derivative and Graph

  1. Oct 4, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f(x,y)=1−x[itex]^{2}[/itex]−y[itex]^{2}[/itex]. Find the point at which

    [itex]\frac{\partial f}{\partial x}[/itex] = [itex]\frac{\partial f}{\partial y}[/itex] = 0
    and illustrate graphically the nature of the surface z = f (x, y) at this point.

    3. The attempt at a solution

    Just did the partial derivatives and got 2x=2y=0 hence x=0 and y=0

    So illustrating z=f(x,y) at this point give z=1

    Creating a contour plot I get the plot attached below.

    This question is part of a difficult assignment I got from uni but this question seems way to easy in comparison to the rest of the assignment. I just want to make sure there isn't something I missed or is it really this simple?

    Thank you

    Attached Files:

    Last edited: Oct 4, 2011
  2. jcsd
  3. Oct 5, 2011 #2
    Any help?
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