A natural cubic spline S is defined by S(x) = { S0(x) = a0 +b0(x ? 1) + d0(x ? 1)3 , if 1 ? x ? 2, S1(x) = a1 + b1(x ? 2) ? 3 4(x ? 2)2 + d1(x ? 2)3 , if 2 ? x ? 3. Use S to interpolate dataf(1) = 1, f(2) = 1, f(3) = 0, find a0, b0, d0, a1, b1, and d1.
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