The cost per unit of a process is modelled by g(x) = (x² + 1)/(x - 1) for x > 1, where x is the…

Step 1. The derivative. $g'(x) = \dfrac{2x(x - 1) - (x^2 + 1)}{(x - 1)^2} = \dfrac{x^2 - 2x - 1}{(x - 1)^2}$.

Step 2. At $x = 3$. $g'(3) = \dfrac{9 - 6 - 1}{4} = \dfrac{1}{2} = 0.5$.

Step 3. Flat points. $x^2 - 2x - 1 = 0$ gives $x = 1 \pm \sqrt{2}$, which is $2.414$ and $-0.414$.

Step 4. The range. Only $x = 2.414$ is greater than $1$.