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Suppose f C 6 (R). Find constants a, b, c so that f (0) = 1 h 2 [cf(2h) bf(h) af(0) bf(h) cf(2h)] O(h 4
Suppose f C 6 (R). Find constants a, b, c so that f (0) = 1 h 2 [cf(2h) bf(h) af(0) bf(h) cf(2h)] O(h 4 ) Hint: N(h) = 1 h2 [f(h) 2f(0) f(h)] satisfies f (0) = N(h) 1 12 f (4)(0)h 2 O(h 4 ), which you may use without proof. Compare N(h) to N(2h)
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