Quote:
Originally Posted by Damian
Suppose the function:
f(x,y) ={ 1 (if x=0 or y=0)
{ 0 (otherwise)
the partial derivatives at the origin are
df/dx = 0 and df/dy = 0
so they exist and are continious.
However the function is not continious in (0,0), so it can't be differentiable there. (there can't be a tangent plane)
What did I misundertood? Because I think the theorem says that if the partial derivatives exists and they are continious then the function is differentiable there.

That function is not differentiable at the origin  just use the definition of derivative in the sense of the limit of the divided difference delta(f)/delta(coordinate)  that limit does not exist at (0,0) in this case.
Also, it makes no sense to speak of a function being continuous at a single point  continuity only makes sense in regions, i.e. neighborhoods of a point.