Answer to Question #8752 in Real Analysis for Joen

Question

Find an approximation to f''(x) using f(x), f(x+h), and f(x+3h).

Answer 1

f"(x) = [ f(x) - 2f(x+h) + f(x+2h) ] / h² + O(h).

For proof, see https://www.geometrictools.com/Documentation/FiniteDifferences.pdf