A function S is defined on the interval [-1,3] by S₁(x), xЄ[-1,0), S(x) = S2(x), xЄ [0,2), S3(r), x € [2,3, where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that must be satisfied if S is a natural cubic spline interpolating the function defined by equations f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = (5)

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