4. Consider the curve defined by y = 40 cos(0.1x + 0.2). The distance d(x) from the origin (0, 0) to a point (x, y) on the curve is d(x) = q x 2 + (40 cos(0.1x + 0.2))2 .

(a) Write a MATLAB program and function M-file to plot d(x) for 100 x 100. Also use the function M-file and the fminbnd command to find (and display) the point (xmin,ymin) on the curve that is closest to the origin and display the minimum distance (i.e., the distance from the origin to the point (xmin,ymin)).

(b) Write a MATLAB program that uses the fzero command to find the point(s) on the curve at a distance of 60 from the origin.