A calculus problem by Harnakshvir Singh Dhillon

Calculus Level 4

Let \(f\) be a differentiable function on the real numbers satisfying, for all real numbers \(x,y\),

\[ f(x+y) = f(x) + f(y) + xy \]

and \(\lim_{h \to 0} \frac{f(h)}{h} = 3\). What is the value of \(f(1)\)?

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