Q. If $f(x) = x^{3} - 6x^{2} + 9x + 3$ be a decreasing function, then $x$ lies in
A) $( - \infty,\ - 1) \cap (3,\ \infty)$
B) $(1,\ 3)$
C) $(3,\ \infty)$
D) None of these
Explanation
(b)
$\because\ \ f(x) = x^{3} - 6x^{2} + 9x + 3$
On differentiating w.r.t. $x$, we get
$f^{'}(x) = 3x^{2} - 12x + 9$
$\Rightarrow \ \ \ f^{'}(x) = 3(x^{2} - 4x + 3)$
For decreasing, $f^{'}(x) < 0$
$\Rightarrow \ \ (x - 3)(x - 1) < 0$,
$\therefore\ \ \ x \in (1,\ 3)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.