For B use MATLAB please

(a) With increment h = 0.1, what is the percent fractional error (compared to the actual derivative) of the second-order-accurate centered finite-difference estimate of the derivative of f(x) = cos() at r = 1? (b) Repeat for the derivative estimated by differentiating the interpolat- ing cubic polynomial (using polyfit, polyder, polyval in Matlab) that goes through the function values at r=0.7.0.9, 1.1, 1.3 (c) Repeat for the derivative estimated using Richardson extrapolation with initial increment ho = 0.4 and 3 levels (i.e. (using the notation in the lecture notes) up to jmax = 2). (a) With increment h = 0.1, what is the percent fractional error (compared to the actual derivative) of the second-order-accurate centered finite-difference estimate of the derivative of f(x) = cos() at r = 1? (b) Repeat for the derivative estimated by differentiating the interpolat- ing cubic polynomial (using polyfit, polyder, polyval in Matlab) that goes through the function values at r=0.7.0.9, 1.1, 1.3 (c) Repeat for the derivative estimated using Richardson extrapolation with initial increment ho = 0.4 and 3 levels (i.e. (using the notation in the lecture notes) up to jmax = 2)