# 4. (a) Assume a function h is differentiable at some point to. Is it true that...

4. (a) Assume a function h is differentiable at some point to. Is it true that h is continuous on some open-neighbourhood of xo? Provide either a proof or a counterexample. (b) Let f be twice differentiable on R and assume that f" is continuous. Show that for all x ER S(x) = S(0) + s°C)x + [ (x - 1))"(dt. (C) Deduce that for any twice continuously differentiable function f on R and any positive x > 0, x € R, there exists some c € (0, 2) such that 2.r - 2t .22 -f"(t) dt

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