Applications Of Derivatives Question 390
Question: The function $ \frac{1}{1+x^{2}} $ is decreasing in the interval
Options:
A) $ (-\infty ,,-1] $
B) $ (-\infty ,,0] $
C) $ [1,\infty ) $
D) $ (0,\infty ) $
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Answer:
Correct Answer: D
Solution:
$ y=\frac{1}{1+x^{2}} $
therefore $ \frac{dy}{dx}=-\frac{2x}{{{(1+x^{2})}^{2}}} $
To be decreasing, $ -\frac{2x}{{{(1+x^{2})}^{2}}}<0 $
therefore $ x>0\Rightarrow x\in (0,\infty ) $ .
BETA
