Suppose that \(f\) satisfies the equation \[f(x+y)=f(x)+f(y)+x^2y+xy^2\]for all real numbers \(x\) and \(y\). Suppose further that\[~~~~~~~~~~~~~\lim_{x\to0}\frac{f(x)}x=1\]a) Find \(f(0)\)
b) Find \(f'(0)\)
c) Find \(f'(x)\)

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I found \(f(0)=0\) but now I am not seeing how to proceed. Just a hint would be nice.

I further think I proved that the function is odd, though I think that doesn't really help me :/

use the definition of a derivative

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