this question has two parts. i have tried to answer part a) but I don't think my proofs are very good. I'm practicing for an exam so if someone could explain the concepts I am supposed to have gotten from the question, I would very much appreciate it.
note: a hint to part a) is that the previous question (which i solved) was to prove f is differentiable at 0 if f(x)=(x^2) for rational x and f(x)=0 for irrational x. I don't think I fully understand the connection to this problem--again, any conceptual help would be much appreciated.
a) let g be a function such that lg(x)l <or= (x^2) for all x. Prove that g is differentiable at 0.
b) this result can be generalized if (x^2) is replaced by lf(x)l where f has what property?