My undergrad analysis is super rusty and I am getting ready for GRE subject and I am completely stuck, I usually have an attempt but I am stuck. However a hint will suffice, I don't need the whole answer. (apparently only 24% get this correct on GRE subject)
Let $f$ and $g$ be continuous functions over the reals s.t.
$g(x) = \int_0^x f(y)(y-x) dy$ $\forall x$
and $g$ is three times continuously differentiable,
what is the greatest integer $n$ s.t. $f$ is $n$ times continuously differentiable?
my guess is using some theorem or lemma or corollary regarding convolutions? is $g$ not a convolution of $f$?
(feel free to edit the title to best fit my question)