A natural cubic spline S is defined by S0(x) = 1+B(x −1)−D(x −1)3, if 1 ≤ x < 2 S1(x) = 1+b(x−2) −3/4(x−2)2 + d(x−2)3, if 2 ≤ x ≤ 3 If S interpolates the data (1, 1), (2, 1), and (3, 0), find B, D, b, and d.

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