Suppose we have an infinitely differentiable function f:(a b) -> R; (x) -> f(x). Let DER(n,f(x)) is the n'th derivative of f at a point x. When does DER(n,f(x)) converge pointwise to a zero function defined on (a b) as n goes to infinity? i.e. What restrictions one can set to the function f so that the derivative sequence of f goes to zero?

thanks in advance for the replies! (Bow)