What is Rolle's theorem generalized into simple words?
I know that the theorem is-
If F:[a,b]-> R a function such that the (n-1) th derivative of F is continuous in [a,b] and (n-1) th derivative is differentiable in (a, b). If F (x) has n + 1 roots in [a,b] then there exists c in (a, b) such that the nth derivative of F (x) at x = c is zero.
I did not really understand that. Can this theorem be further simplified?
I know Rolle's theorem but I am confused in its generalization.