Determine the value of the coefficients  a, b, c, d and e such that the following f(x) is a natural cubic spline on; f(x) = a + b(x−1) + c(x−1)2 + d(x−1)3     x ∈ [0,1] f(x) = (x−1)3 + ex2 −1     x ∈ [1,2]

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A: The details solution of the given question is given below in step 2.

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A: Differentiating with respect to x, we get Again differentiating with respect to x, we get