Let f be the function defined by f(x) = e*cos x. (a) Find the average rate of change of f on the interval O S x S n. (b) What is the slope of the line tangent to the graph of fat x = 3 7t ? (c) Find the absolute minimum value of f on the interval 0 S x S 2x. Justify your answer. (d) Let g be a differentiable function such that g = 0. The graph of g', the derivative of g, is shown below. Find the value of lim f(x) or state that it does not exist. Justify your answer. X->x/2 8(x) Graph of g