Let f:R to R be a function such that f(x...

Let `f:R to R` be a function such that `f(x+y)=f(x)+f(y)"for all", x,y in R`
If f(x) is differentiable at x=0. then, which one of the following is incorrect?

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 at finitely many points

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The correct Answer is:

B, C

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