Question: If f'' is continuous, show that f(x + h) 2f(x) + f(x h) h? lim %3| = f(x)

If f'' is continuous, show that

f(x + h) – 2f(x) + f(x – h) h? lim %3| = f

(a) Use the definition of derivative to compute f'(0).
(b) Show that f has derivatives of all orders that are defined on R.

f(x + h) 2f(x) + f(x h) h? lim %3| = f"(x)

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