The function 1 1 + x^2 is decreasing in the interval - Vidyadip

MCQ

The function ${1 \over {1 + {x^2}}}$ is decreasing in the interval

A
$( - \infty ,\, - 1]$
B
$( - \infty ,\,0]$
C
$[1,\infty )$
✓
$(0,\infty )$

✓

Answer

Correct option: D.

$(0,\infty )$

d
(d) $y = \frac{1}{{1 + {x^2}}}$==>$\frac{{dy}}{{dx}} = - \frac{{2x}}{{{{(1 + {x^2})}^2}}}$

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

==>$x > 0 \Rightarrow x \in (0,\infty )$.

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