(3) B-spline. Derive the explicit formulas for A(x), B(x), C(x), D(x), and then the piecewise cubic...

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(3) B-spline. Derive the explicit formulas for A(x), B(x), C(x), D(x), and then the piecewise cubic polynomial on the interval [1,2] for the B-spline. (The piecewise cubic polynomial on the interval [2, 3] is given by symmetry: Y23(x) = Y12(4x).) Hint: On [1,2], (xa, Ya) = (1, 1), y = 6, (x, Y) = (2,4), y = 12. (3) B-spline. Derive the explicit formulas for A(x), B(x), C(x), D(x), and then the piecewise cubic polynomial on the interval [1,2] for the B-spline. (The piecewise cubic polynomial on the interval [2, 3] is given by symmetry: Y23(x) = Y12(4x).) Hint: On [1,2], (xa, Ya) = (1, 1), y = 6, (x, Y) = (2,4), y = 12.