(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

Repeat Exercise 15, constructing instead the clamped cubic spline with
0. Use the derivatives of the spline to approximate f'(0.5) and f'' (0.5). Compare these approximations to the actual values.