I am not too sure about how I should approach this question, but it seemed like an interesting one when I discovered it.
2026-04-18 02:57:02.1776481022
Find $h(x) = x f(x)$, if $f (0) = -2$, and $f'(0) = 3$.
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Assuming $f$ is analytical at zero, you know that $$ f(x)=-2+3x+x^2g(x) $$ for any $g$ analytical at zero. Now $$ h(x)=xf(x)=-2x+3x^2+x^3g(x). $$ Without more information, all you can discover here is $h(0)$, $h'(0)$ and $h''(0)$.