(Solution) - Repeat Exercise 15 constructing instead the clamped cubic spline with -(2025 Original AI-Free Solution)

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Repeat Exercise 15, constructing instead the clamped cubic spline with f'(0) = f' (1) = 0.
In Exercise 15
Construct a natural cubic spline to approximate f (x) = cos ?x by using the values given by f (x) at x = 0, 0.25, 0.5, 0.75, and 1.0. Integrate the spline over [0, 1], and compare the result to

0. Use the derivatives of the spline to approximate f'(0.5) and f'' (0.5). Compare these approximations to the actual values.