Let f:R→R be a function such that
f(x+y)=f(x)+f(y),∀x,y∈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 for all x∈R
c. f′(x) is constant for all x∈R
d. f(x) is differentiable except at finitely many points