(4) Suppose that (7) If f (x) is a differentiable functions, find the derivative of the function u (z) = f(x)g(x) and v (2) = J(2) g (x) In other words, find a2. Your answer should be in terms of x, f (r) , and f' (x). Simplify your where f (x) and g (x) are graphed below (the graph of f is blue, the graph of g is red) answer. (a) Find u' (4). Show how you get your answer. (8) A ball is thrown straight up into the air. It's height h in meters after t seconds is given by h (t) = -5t2 + 22t + 4 (b) Find v' (1). Show how you get your answer. Include units when answering the following questions. Justify your answers. (a) What is the height of the ball at t = 0 seonds? (b) What is the velocity of the ball at t = 0 seconds? (5) Differentiate the following. Simplify answers as appropriate. = ex +2 (c) What is the velocity of the ball at t = 2 seconds? ( b) f (t ) = 13+1+1 (d) What is the acceleration of the ball at t = 2 seconds? ( c) f (t ) = ty (6) Let f (x) = x3el. Find both f' (x) and f" (x)