1) If f(x)=xx2+1 is increasing function , then the value of x lies in A) R B) (-∞,-1) C) (1, ∞,) D) (-1,1) Answer: Option DExplanation: Given, f(x)=xx2+1 ⇒ f′(x)=(x2+1)×1−x(2x)(x2+1)2 =(x2+1−2x2)(x2+1)2=1−x2(x2+1)2 since, f(x) is increasing function, ∴ f '(x) >0 ⇒ 1−x2(x2+1)2>0 ⇒ 1−x2>0 ⇒ x2<1 ⇒ -1 < x< 1 ∴ x ε (-1,1) Hence, option (d) is correct.