What is the absolute minimum value of $f(x)=x+\dfrac{1}{x}$ on $\left[\dfrac{1}{2},2\right]$?

Core Concept

$f'(x)=1-\frac{1}{x^2}$ gives the critical point $x=1$. The candidates are $f(\frac{1}{2})=\frac{5}{2}$, $f(1)=2$, and $f(2)=\frac{5}{2}$, so the minimum value is $2$.