Question

If $f\left(x\right)=x^3-6x^2-36x+2$ is decreasing function, then $x$ belongs to

• A. $(6,\infty )$
• B. $(-\infty ,-2)$
• C. $(-2,6)$
• D. None of the above

Answer 1

The correct option is C $(-2,6)$

Given, $f\left(x\right)=x^3-6x^2-36x+2$
On differentiating w.r.t. $x$, we get
$f^{\prime }\left(x\right)=3x^2-12x-36$
For decreasing, $f^{\prime }\left(x\right)<0$
$\Rightarrow 3(x^2-4x-12)<0$
$\Rightarrow (x-6)(x+2)<0$
$\Rightarrow -2<x<6$
$\therefore xϵ(-2,6)$.