\( f(x+y)=f(x)+f(y)+|x| y+x y^{2} \) for all \( x, y \in R \) and \( f^{\prime}(0)=0 \) (A) \( f...
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0\( f(x+y)=f(x)+f(y)+|x| y+x y^{2} \) for all \( x, y \in R \) and \( f^{\prime}(0)=0 \)
(A) \( f \) need not be differentiable at every non-zero \( x \)
(B) \( f \) is differentiable for al \( x \in R \)
(C) \( f \) is twice differentiable at \( x=0 \)
(D) none of these
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