A function $f$ is **strictly increasing** on an interval if, on that interval:

$f'(x) > 0$ throughout an open interval ⇒ strictly increasing there. $f'(x) < 0$ ⇒ strictly decreasing. $f'(x) = 0$ at isolated points OK (e.g., $x^3$ is strictly increasing even though $f'(0) = 0$).