If , and ,…

MATHEMATICS · Single correct · AoPS · Mathematics · Functions · More Variables

Problem

If f(x+y)=f(x)+f(y)+∣x∣y+xy2f(x+y) = f(x) + f(y) + |x|y + xy^2 , ∀x,y∈R\forall x, y \in \mathbb{R} and f′(0)=0f'(0) = 0 , then (1) ff need not be differentiable at every non-zero xx (2) ff is differentiable for all x∈Rx \in \mathbb{R} (3) ff is twice differentiable at x=0x = 0 (4) None of the above

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