For which interval the given function f(x) = - 2 x^3 - 9 x^2 - 12… - Vidyadip

MCQ

For which interval the given function $f(x) = - 2{x^3} - 9{x^2} - 12x + 1$ is decreasing

A
$( - 2,\,\infty )$
B
$( - 2,\, - 1)$
C
$( - \infty ,\, - 1)$
✓
$( - \infty ,\,\, - 2)$ and $( - 1,\,\infty )$

✓

Answer

Correct option: D.

$( - \infty ,\,\, - 2)$ and $( - 1,\,\infty )$

d
(d) $f(x) = - 2{x^3} - 9{x^2} - 12x + 1$

==>$f'(x) = - 6{x^2} - 18x - 12$

To be decreasing $f'(x) < 0$, $i.e.,$ $ - 6{x^2} - 18x - 12 < 0$

==>${x^2} + 3x + 2 > 0$==>$(x + 2)(x + 1) > 0$

Therefore either $x < - 2$ or $x > - 1$

==>$x \in ( - 1,\infty )$ or $( - \infty , - 2)$.

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