How do we find all possible values of r

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$f'(x)=2rx^{2r-1}arctan(\frac{1}{x})-\frac{x^{2r}}{1+x^2}$ Since $arctan(\frac{1}{x})$ is finite, $f'(0)=0$ for all $r\gt \frac{1}{2}$. I don't see the restriction to $Q^+$.