The function f(x) = x^3 + 3x is increasing in interval:

The correct answer is Option (3) → $\mathbb{R}$ ##

$f(x) = x^3 + 3x$

$f'(x) = 3x^2 + 3$

For increasing, $f'(x) > 0$

$3x^2 + 3 > 0 \quad (x \in \mathbb{R} : x^2 > 0)$