Question

The function $f\left(x\right)=\frac{1}{1+x^2}$ is decreasing in the interval

• A. $(-\infty ,-1]$
• B. $(-\infty ,0]$
• C. $[1,\infty )$
• D. $(0,\infty )$

Answer 1

Answer: (A)

$(-\infty ,-1]$

$f^{\prime }\left(x\right)=\frac{(1+x^2\times 0)-1\left(2x\right)}{(1+x^2{)}^2}$

for $\frac{-2x}{(1+x^2{)}^2}<0,-2x<0$ $x<0,$

For$(-\infty ,-1),f\left(x\right)$ is decreasing