Chapter 4 - Applications of the Derivative - 4.2 What Derivatives Tell Us - 4.2 Exercises - Page 256: 21

$f$ is increasing on $(-\infty,1/2)$, $f$ is decreasing on $(1/2, \infty)$.

$f'(x) = 1 − 2x$, which is $0$ when $x = 1/2$. On $(-\infty,1/2)$, $f' > 0$ so $f$ is increasing on this interval, while on $(1/2,∞)$, $f' < 0$, so $f$ is decreasing on this interval.