Question: Construct a natural cubic spline to approximate f (x) = cos x by using the values given by f (x) at x = 0, 0.25,

Construct a natural cubic spline to approximate f (x) = cos Ï€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.

la cos Tx dx =

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