The interval on which the function $f(x) = 2x^3 + 9x^2 + 12x - 1$ is decreasing is
Answer & explanation
Correct answer: option 2
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 $[-2, -1]$.