Data is fitted to a cubic f = ax 3 + bx 2 + cx + d
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Data is fitted to a cubic f = ax3 + bx2 + cx + d with the slope of the curve given by f' = 3ax2 + 2bx + c If f1 = f(x1), f2 = f(x2), f '1 = f'(x1) and f´2 = f´(x2), show that fitting the data gives the matrix equation for a, b, c and d as
Use Gaussian elimination to evaluate a, b, c and d. For the case
evaluate a, b, c and d. Plot the cubic and estimate the maximum value of f in the region 0 1. Note that this exercise forms the basis of one of the standard methods for finding the maximum of a function f(x) numerically.
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