can someone give me an example of a function all of whose directional derivatives at 0 are 0 but is....?

Question

discontinuous at 0

Answer 1

If the derivatives are *exactly* zero, @ zero, then it's not discontinuous. If the derivative is indeterminant, but d/dx x+ and d/dx x- are 0 would be something like the heaviside function of x.

Answer 2

An example here:
http://www.mathreference.com/ca-mv,part.html