Suppose that we did not know (6.2.15) but thought it possible to approximate d2f
Chapter 6, Problem 6.2.4(choose chapter or problem)
Suppose that we did not know (6.2.15) but thought it possible to approximate d2f /dx2(x0) by an unknown linear combination of the three function values, f(x0 x), f(x0), and f(x0 + x): d2f dx2 af(x0 x) + bf(x0) + cf(x0 + x). Determine a, b, and c by expanding the right-hand side in a Taylor series around x0 using (6.2.10) and (6.2.11) and equating coefficients through d2f /dx2(x0).
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