Q. $f(x) = x^{3} - 6x^{2} - 36x + 2$ is decreasing function, then $x \in$
A) $(6,\ \infty)$
B) $( - \infty,\ - 2)$
C) $( - 2,\ 6)$
D) None of these
Explanation
(c)
Given, $f(x) = x^{3} - 6x^{2} - 36x + 2$
$f^{'}(x) = 3x^{2} - 12x - 36$
For decreasing, $f^{'}(x) < 0$
$\Rightarrow \ \ \ 3\left( x^{2} - 4x - 12 \right) < 0$
$\Rightarrow \ \ \ (x - 6)(x + 2) < 0$
$\Rightarrow \ \ - 2 < x < 6$
$\Rightarrow \ \ \ x \in ( - 2,\ 6)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.