User:Pt18378193/Finding the minima of (x^2+1)/x with x larger or equal to 2

5/2. Why?

The derivative of $f={\frac {x^{2}+1}{x}}$is $1-{\frac {1}{x^{2}}}$.

The critical points of $f$ are $\{-1,1\}$.

The extrema(s) of $f$ can only occur at the critical points (outside the domain,ignored) or the endpoints of the domain:$2$ and $\infty$.

Critical points	$f$	Conclusion
2	${\frac {5}{2}}$	Local min
$\infty$	$\infty$	(Local max,ignored)