Question

If $f\left(x\right)=\frac{x}{x^2+1}$ is increasing function then the value of $x$ lies in

• A. $R$
• B. $(-\infty ,-1)$
• C. $(1,\infty )$
• D. $(-1,1)$

Answer 1

The correct option is D $(-1,1)$

Given function is $f\left(x\right)=\frac{x}{x^2+1}$,

Given that this is increasing in nature,

$⟹f^{{}^{\prime }}\left(x\right)>0⟹\frac{1-x^2}{{(1+x^2)}^2}>0⟹x^2<1$

$x$ lies in the interval $(-1,1)$.