need help with this

Suppose that f is dened in neighborhood of a\": and f\"(s:) exists. Show that m for + h) are) + m: h) hrO '22 = m) (Hint use Theorem 5.8). Now consider the function f(:13) = m\" . the above limit exist? Does f\" (0) exist? Does Theorem 5.8 (L'Hopital) Let f and g be real-valued differentiable functions defined on an interval (a, b). Assume that g'(x) # 0 for all x E (a, b), and that the following two conditions are satisfied f' (ac) (1) lim (2) lim g(x) = lim f(x) = 0. rag'(x) = A, f (30) Then lime-a g(x) = A. In this theorem a, b, A are extended real numbers, that is, they may be too. Condition (2) can be replaced by limx-a g(x) = too, and the conclusion is still true