If $f(x+y) = f(x)+f(y)+x^2y+xy^2$ and $\lim_{x\to0} \frac{f(x)}{x}=1, (x,y \in R)$, find $f(0),f'(0),f'(x)$
How do I find $f(0)$, $f'(0)$, and $f'(x)$ given $f(x+y)=f(x)+f(y)+x^2y+xy^2$ and $\lim_{x\to0}\frac{f(x)}{x}=1$?