Assume that f, g are functions that are continuous and nonnegative for x ≥ 0, differentiable for x > 0, f(0) = 0 = g(0) and g(x) 6= 0 for x > 0. If f ' is monotonically increasing and g ' is monotonically decreasing, then show that f(x) / g(x) is monotonically increasing for x > 0.