The function f(x)=(9-x2)2 increases in
(-3,0)∪(3,∞)
(-∞,-3)∪(3,∞)
(-∞,-3)∪(0,3)
(-3,3)
(3,∞)
Explanation for correct option
Given function f(x)=(9-x2)2
⇒f'(x)=2(9–x2)(-2x)
The function f(x) will be increasing if f'(x)>0
⇒2(9–x2)(-2x)>0⇒2(32–x2)(-2x)>0⇒2(3-x)(3+x)(-2x)>0⇒(3-x)(3+x)(-2x)>0
Thus, f(x) is increasing in x∈(-3,0)∪(3,∞)
Hence, OptionA is correct.