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Let \( t: R \rightarrow R \) 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
(A) \( f(x) \) is differentiable only in a finite interval containing zero
\( \mathrm{P} \)
(B) \( f(x) \) is continuous \( \forall x \in \mathbf{R} \)
W
(C) \( f^{\prime}(x) \) is constant \( \forall x \in \mathbf{R} \)
(D) \( f(x) \) is differentiable except at finitely many points
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