Q. The function $f$ defined by $f(x) = x^{3} - 6x^{2} - 36x + 7$ is increasing, if
A) $x > 2$ and also $x > 6$
B) $x > 2$ and also $x < 6$
C) $x > - 2$ and also $x < 6$
D) $x < - 2$ and also $x > 6$
Explanation
(d)
Given $f\ (x) = x^{3} - 6x^{2} - 36x + 7$
$\Rightarrow f^{'}(x) = 3x^{2} - 12x = 36$
For $f(x)$to be increasing, $f’(x) > 0$
$\Rightarrow 3(x^{2} - 4x - 12) > 0$
$\Rightarrow (x - 6)(x + 2) > 0$
$\Rightarrow x > 6$
And $x < - 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.