Chapter 4 - Applications of the Derivative - 4.2 What Derivatives Tell Us - 4.2 Exercises - Page 257: 34

$f$ is decreasing on $(0, 1)$ and increasing on $(1,∞)$.

$f'(x) = 2x − \frac{2}{x} = \frac{2(x^2−1)}{x}$ which is $0$ for $x =\pm1$. Note that the domain of $f$ is $(0,∞)$ and that $f'(1/2) = −3 < 0$ and $f'(2) = 3 > 0$, so $f$ is decreasing on $(0, 1)$ and increasing on $(1,∞)$.