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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 D

Explanation:

 Given, f(x)=xx2+1

     f(x)=(x2+1)×1x(2x)(x2+1)2

=(x2+12x2)(x2+1)2=1x2(x2+1)2

since, f(x)  is increasing function,

     f '(x)  >0

    1x2(x2+1)2>0

  1x2>0

    x2<1

   -1 < x< 1

   x ε  (-1,1)

  Hence, option (d)  is correct.