# Partial Derivative and Graph

1. Oct 4, 2011

### KingBigness

1. The problem statement, all variables and given/known data

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

$\frac{\partial f}{\partial x}$ = $\frac{\partial f}{\partial y}$ = 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:

• ###### MSP241419hb99bd9ig0gh4i00004aa457092c3a6ee2.gif
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Last edited: Oct 4, 2011
2. Oct 5, 2011

### KingBigness

Any help?

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