Suppose that \( f \) is a differentiable function with the property...

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Suppose that \( f \) is a differentiable function with the property that \( f(x+y)=f(x)+f(y)+x y \) and \( f^{\prime}(0)=5 \) then
(a) \( f \) is a linear function
(b) \( f(x)=3 x+x^{2} \)
(c) \( f(x)=5 x+x^{2} / 2 \)
(d) \( f(x)=x+\frac{5 x^{2}}{2} \)
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