The interval on which the function $f(x) = 2x^3 + 9x^2 + 12x - 1$ is decreasing is

$[-2, -1]$

The correct answer is Option (2) → $[-2, -1]$ ##

We have, $f(x) = 2x^3 + 9x^2 + 12x - 1$

$∴f'(x) = 6x^2 + 18x + 12$

$= 6(x^2 + 3x + 2) = 6(x + 2)(x + 1)$

So, $f'(x) \leq 0$, for decreasing.

On drawing number line as below:

We see that $f'(x)$ is decreasing in $[-2, -1]$.