question_answer

The function\[f(x={{(9-{{x}^{2}})}^{2}}\]increases in

A)  \[(-3,0)\cup (3,\infty )\]

B)  \[(-\infty ,-3)\cup (3,\infty )\]

C)  \[(-\infty ,-3)\cup (0,3)\]

D)  \[(-3,3)\]

E)  \[(3,\infty )\]

Correct Answer: A

Solution :

Given, \[f(x)={{(9-{{x}^{2}})}^{2}}\] On differentiating w.r.t.\[x,\]we get \[f(x)=2(9-{{x}^{2}})(-2x)\] Now, put \[f(x)=0\] \[\Rightarrow \]               \[2(9-{{x}^{2}})(-2x)=0\] \[\Rightarrow \]               \[x=0,\pm 3\]                 \[\therefore \]\[f(x)\]is increasing in\[(-3,0)\cup (3,\infty )\].