Any help with this is greatly appreciated!

1) Let f(x) = (x^4(2 + sin(1/x)) if x=/ 0, f(x) = 0 if x = 0.(a) Prove that f is differentiable on R.(b) Prove that f has an absolute minimum at x = 0.(c) Prove that f' takes on both positive and negative values in every neighbourhood of 0. That is, prove that, for every > 0, f' takes on both positive and negative values in the interval (, ).

2) Suppose f : R R is continuous and limx f(x) and limx f(x) both exist. Prove that f is bounded.