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Let R rarr R be a function such that f(x...

Let `R rarr R` be a function such that `f(x+y) = f(x)+f(y) AA x, y in R`. If f(x) is differentiable at x= 0, then

A

f(x) is differentiable only in a finite interval containing zero

B

f(x) is continuous `AA x in R`

C

f'(x) is constant `AA x in R`

D

f(x) is differentiable except a finitely many points

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B, C
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