Q. The function $f(x) = \left( 9 - x^{2} \right)^{2}$ increasing in
A) $( - 3,\ 0) \cup (3,\ \infty)$
B) $( - \infty,\ - 3) \cup (3,\ \infty)$
C) $( - \infty,\ - 3) \cup (0,\ 3)$
D) $( - 3,\ 3)$
Explanation
(a)
Given, $f(x) = \left( 9 - x^{2} \right)^{2}$
$\Rightarrow \ \ \ f^{''}(x) = 2\left( 9 - x^{2} \right)( - 2x)$
Now, put $f^{''}(x) = 0$
$\Rightarrow \ \ \ \ 2\left( 9 - x^{2} \right)( - 2x) = 0\ \ \ \Rightarrow \ \ \ x = 0,\ \pm 3$
[image:6_image18.emf]
$\therefore\ \ \ f^{''}(x)$ is increasing in $( - 3,\ 0) \cup (3,\ \infty)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.