Consider the function f(x) = x 2cosx on the interval [2z, 27]. a) b) c) d) e) Sketch the graphs of y = x and y = 2 cos x on [2m, 271]. How many points of intersection (i.e. zeros of f) occur on this interval? Using Calculus methods that we learned in class, determine any relative extremes and points of inflection of y = f(x) on the interval [27, 27]. Sketch the graph of f(x) on [2r7, 2m]. Hint: First note where f (x) = 0 (using part a) and where f(x) = x. Explain why the sketch from part c lies between the lines y = x 2 and y = x + 2. Add these lines to the sketch, showing clearly where f(x) meets these lines. Make a sketch, similar to the one in part d, showing your prediction for the general case of the graph y = x ccosx, based on your work in this task, for EACH of the following cases: e O0l