1. The problem statement, all variables and given/known data Suppose f and g are differentiable on R, and f(a) = g(a) and f'(x) <= g'(x) for all x >= a. Show that f(x) <= g(x) for all x >= a. Give a physical interpretation of this result. Also, using the Mean Value Theorem: (a) Let f: R --> R be a differentiable function. Suppose that its derivative f'(x) is bounded Prove that f is uniformly continuous. (b) Let f: R --> R be a differentiable function. Suppose that lim (x --> infinity) f'(x) = infinity. Show that f cannot be uniformly continuous. (c) Let g(x) = (x)^1/2 show that g'(x) is unbounded on (0,1] but g(x) is uniformly continuous on [0,1]. 2. Relevant equations 3. The attempt at a solution I don't know how to quite formulate the inequalities, any help?