Question: The following data were generated with the fifth order polynomial: f(x) = 0.0185x 5 0.444x 4 + 3.9125x 3 15.456x 2 + 27.069x

The following data were generated with the fifth order polynomial: f(x) = 0.0185x⁵ − 0.444x⁴ + 3.9125x³ − 15.456x² + 27.069x − 14.1:

X 1 f(x) 1.000 3 2.172 5 4.220 6 7 5.430 4.912 (a) Fit these data with a cubic spline with not-a-knot end conditions. Create a plot comparing the fit with the function.
(b) Repeat (a) but use clamped end conditions where the end slopes are set at the exact values as determined by differentiating the function.

X 1 f(x) 1.000 3 2.172 5 4.220 6 7 5.430 4.912 9 9.120

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