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 $$\infty$$.