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Let f : R rarr R be a function such that...

Let `f : 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 epsilonR`

C

`f'(x)` is constant `AA x epsilonR`

D

`f(x)` is differentiable except at finitely many points

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The correct Answer is:
B, C
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