Mr. Benorin, you see, this is a local problem: the final result is evaluated at x = a. Besides that, f satisfies some particular conditions, which must be considered:
(a) f(x) \neq 0, over some open interval A;
(b) f is a series of even powers;
(c) f^{(2n+1)}(a) = 0 and f^{(2n)}(a) \neq 0, n...