I am unsure of the relationship between a gradient vector and the surface itself. In this case, F is a continuously differentiable, real-valued function, and p is a point on the level set M where F = c.
In the case where ∇F(p) = 0, is it true that M must have a singularity at p? Why?
Also, does this relationship work the other way? If M has a singularity at p, must the gradient ∇F(p) have a value of zero?
