Let f :R - R,f(x) = sin (x)cos(x) Part of the graph of f is shown below. 0.5 -0.5 a. State the period of f. b. State the range off. c. Find the general solution for the x intercepts of f. Now consider the graph of h(x) = log, (sin*(x)cos(x)). d. Find the maximal domain of h. Part of the graph of the derivative of f is shown below. The points A, B and C are at the turning points of the graph of S' . 1.5 4 e. Find the equation of the line which passes through AB. f. i. Find the equation of the perpendicular bisector of the line segment AB. ii. Show that the perpendicular bisector does not pass through the point C. g. Find the area bounded by the graphs of f and f' over the interval [0,2x]. Give your answer correct to two decimal places. Now consider the family of curves g(x) = f (kx ), where ke R'. h. Find the area bounded by the graphs of g and g' over one cycle, if the period of g is 4x . Give your answer correct to two decimal places. i. Find the smallest integer value of & for which the area bounded by the graphs of g and g' over one cycle, is less than 3.1