Question

Consider the function
$f\left(x\right)=-2x^3-9x^2-12x+1$
The function $f\left(x\right)$ is an increasing function in the interval

• A. $(-2,-1)$
• B. $(-\infty ,-2)$
• C. $(-1,2)$
• D. $(-1,\infty )$

Answer 1

The correct option is A $(-2,-1)$

Solution:

Given that:

$f\left(x\right)=-2x^3-9x^2-12x+1$

On differentiating both sides w.r.t x. we get

$f^{\prime }\left(x\right)=-6x^2-18x-12$

For $f\left(x\right)$ to be increasing $f^{\prime }\left(x\right)>0$

$\therefore -6x^2-18x-12>0$

$⟹x^2+3x+2<0⟹(x+1)(x+2)<0$

$\therefore -2<x<-1$

Hence, A is the correct option.