Let $f:R\rightarrow R$ be a function such that $f(x+y)=f(x)+f(y)\forall x,y\in R$ if $f(x)$ is differentiable at $x=0$ then

Question

$\begin{array}{1 1}(a)\;f(x)\;is\;differentiable\;only\;in\;a\;finite\;interval\;containing\;zero\\(b)\;f(x)\;is\;continuous\;\forall\;x\in R\\(c)\;f'(x)\;is\;not\;constant\;\forall\;x\in R\\(d)\;f(x)\;is\;differentiable\;except\;at\;finitely\;many\;points\end{array}$