If I have a function f(x,y) that is not constant and has no 0 derivative in every direction and I want to see if it is differentiable at a certain point
Example, I want to see if this function is differentiable in (0,0) $$\ f(x,y)= \sqrt{x^2 + y^2} $$
The derivate of f in direction of versor (u,v) is: $$\lim_{h->0} \frac{{f(hu,hv)}-f(0,0)}{h} = \sqrt{u^2 + v^2} $$
if this is equals to zero for more than 2 versors
knowing that a function has two directions of zero derivative (there are two vectors perpendicular to the gradient at that point)
is it valid to prove that if there are more than two directions equal to zero at that point then it is not differentiable at that point?
