$f(x) = x^3 + ax^2 + 3x + 1$ is increasing on $\mathbb{R}$. Which condition must $a$ satisfy?

Explanation

1. 01

   $f'(x) = 3x^2 + 2ax + 3$ must be $\ge 0$ for every $x$: its discriminant must be $\le 0$.

2. 02

   $4a^2 - 36 \le 0$, so $a^2 \le 9$: $-3 \le a \le 3$.