Q .     Let `f:\mathbb{R} \rightarrow \mathbb{R} ` be a function such that `f(x+y)=f(x)+f(y),\ \forall x,\ y\in \mathbb{R}.`
lf `f(x)` is differentiable at `x=0`, then

JEE 2011 ADVANCED Paper - 1

(This question may have multiple correct answers)

A f(x) is differentiable only in a finite interval containing zero
B f(x) is continuous `\forall x\in \mathbb{R}`
C f'(x) is constant `\forall x\in \mathbb{R}`
D f(x) is differentiable except at finitely many points

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