Repeat Exercise 16, constructing instead the clamped cubic spline with f'(0) = 1, f'(1) = e1. In

Repeat Exercise 16, constructing instead the clamped cubic spline with f'(0) = ˆ’1, f'(1) = ˆ’eˆ’1.
In Exercise 16
Construct a natural cubic spline to approximate f (x) = eˆ’x by using the values given by f (x) at x = 0, 0.25, 0.75, and 1.0. Integrate the spline over [0, 1], and compare the result to

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

Transcribed Image Text:

Ge* dx = 1 - 1/e.