# Thread: Points on a surface and differentiability.

1. ## 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 .
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2. Originally Posted by zpwnchen
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 .
Differentiate implicitly to find $\displaystyle \frac{\partial z}{\partial x}$ and $\displaystyle \frac{\partial z}{\partial y}$ and find where they are undefined. (This will be when the denominator is $\displaystyle 0$.) Since there are no terms containing $\displaystyle x$, $\displaystyle y$, and $\displaystyle z$, the denominators for both partial derivatives will be the same. If my calculations are correct, you should get:
$\displaystyle g(x,y,z)=x^6+y^3\cos(y^3 z^3)=0$