When a company produces and sells x thousand units per week, its total weekly profit is P thousand dollars, where P = 200x / (100 + x2). The production level at t weeks from the present is x = 4 + 2t. (a) Find the marginal profit, dP/dx. (b) Find the time rate of change of profit, dP/dt. (c) How fast (with respect to time) are profits changing when t = 8?