Numerical Methods Question: Will need matlab!!!! (a) Construct a free cubic spline to approximate f(x) = e^-x by using the values given by f(x) at x = 0, 0.25, 0.75, and x= 1.0. (You may use Matlab to solve the linear system). 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. (b) Compute the polynomial interpolant of degree three that passes through the above four data points. (c) Plot the two interpolants you found on the same graph (using the Matlab commands plot) (d) Plot the errors in the two interpolants on the same graph (using the Matlab commands plot). What are your observations?

e-I dr = 1-1/e 0