Limits Plus: IV

Calculus Level 3

Suppose \(f\) is a function that satisfies the equation

\(f(x+y)=f(x)+f(y)+x^2y+xy^2\)

for all real numbers \(x\) and \(y\). Suppose also that

\(lim_{x\rightarrow 0}{\frac{f(x)}{x}}=1\).

Evaluate \(f(0)+f'(0)+f'(x)-x^2\).

NOTE: No L'Hôpital's Rule is allowed.


Problem credit: Calculus: 6E, James Stewart

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