Let $f(x) = \dfrac{2x^2 + 3x + 1}{2x - 1}$. Find the maximum and minimum values of $f$ on $[2, 3]$.
Setting $f'(x) = 0$ gives $4x^2 - 4x - 5 = 0$, whose roots are outside $[2,3]$. $f'(x) > 0$ on $(2,3)$, so $f$ is increasing. $f(2) = 5$ and $f(3) = 28/5$. Maximum is $28/5$ and minimum is $5$. (C)
Let $f(x) = \dfrac{2x^2 + 3x + 1}{2x - 1}$. Find the maximum and minimum values of $f$ on $[2, 3]$.