Let $f : R \to R$ be a differentiable function satisfying $f (x + y) = f (x) + f (y) + x^{2} y + x y^{2}$ for all real numbers x and y. If $x \to 0 lim \frac{f ( x )}{x} = 1,$ then
The value of f'(3) is

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Let

f : R \to R

be a differentiable function satisfying

f (x + y) = f (x) + f (y) + x^{2} y + x y^{2}

for all real numbers x and y. If

x \to 0 lim \frac{f ( x )}{x} = 1,

then
The value of f'(3) is

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Question Text

Let

f : R \to R

be a differentiable function satisfying

f (x + y) = f (x) + f (y) + x^{2} y + x y^{2}

for all real numbers x and y. If

x \to 0 lim \frac{f ( x )}{x} = 1,

then
The value of f'(3) is

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