2. (10 marks) Suppose we have a natural spline: a1 +25x+9x+x S(x) = 26+ a2x+a3x -...

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2. (10 marks) Suppose we have a natural spline: a1 +25x+9x+x S(x) = 26+ a2x+a3x - x 2619x+a4x + 15 -163+208x60x + a6x x = [-3, -1] x = [1,0] x = [0,3] x = [3,4] (a) Determine the values of a1, a2, a6. ... (b) Using the Lagrange basis, construct a cubic interpolation polynomial which interpolates the values of S(x) at -3, -1, 0, 3. (You can use symbolic values of S(x) to complete this part.) 2. (10 marks) Suppose we have a natural spline: a1 +25x+9x+x S(x) = 26+ a2x+a3x - x 2619x+a4x + 15 -163+208x60x + a6x x = [-3, -1] x = [1,0] x = [0,3] x = [3,4] (a) Determine the values of a1, a2, a6. ... (b) Using the Lagrange basis, construct a cubic interpolation polynomial which interpolates the values of S(x) at -3, -1, 0, 3. (You can use symbolic values of S(x) to complete this part.)