Find the polynomial of degree 7 that interpolates the function arctan at the 10 equally-spaced points [1:.5:4] (you may use any interpolation process but you are not allowed, however, to use the matlab library m-file polyfit.m). Then compute the error over the interval [1, 7] (i.e., evaluate the error on a fine mesh on the interval [1, 7]. The matlab command linspace(-1,7) generates such mesh). Try then to see whether similar results are obtained if you increase the number of interpolation points and/or change the function you interpolate. Turn in your code, your output, and a brief account of the conclusions you drew from this experiment.