If $x$ is a positive real number, find the smallest possible value of $2 x+\frac{18}{x}$.
The answer is 12 . This is achieved when $x=3$; to see it is optimal, note that $2 x+\frac{18}{x} \geq 6 \Longleftrightarrow x^{2}-6 x+9 \geq 0$, which is obviously true since the left-hand side is $(x-3)^{2} \geq 0$.

Alternatively, those who know the so-called AM-GM inequality may apply it directly.