Final answer:
To create clamped cubic splines for given data, ensure smoothness by specifying derivatives at endpoints. At x=0.8 and x=1.0, set f′ to 2.1691753 and −0.625, respectively. At x=0 and x=0.5, set f′ to 2 and 5.43656. At x=0.1 and x=0.3, set f′ to −2.8004996 and −2.9734038 for continuity.
Step-by-step explanation:
To construct clamped cubic splines for the given data, ensure the splines are smooth by considering the derivatives at the endpoints.
A. At x=0.8, set f′=2.1691753, and at x=1.0, set f′=−0.625 to ensure continuity.
B. At x=0, set f′=2, and at x=0.5, set f′=5.43656 for smoothness.
C. At x=0.1, set f′=−2.8004996, and at x=0.3, set f′=−2.9734038 to maintain spline continuity.
These steps ensure the clamped cubic splines interpolate the data points smoothly with specified derivatives at the endpoints.