Solve the below:
Q: Suppose f:R→R is twice differentiable with both f' and f'' continuous in an interval around 0. Suppose further that f(0)=0. Let
h(x)= {(f(x)/x, if x≠0, f' (0), if x=0.)
Show that
h is differentiable at x=0.
h is differentiable at x=0 with h' (0)=1/2 f'' (0).
h' is continuous at x=0.