The function x + 1 x ,(x 0) is a non-increasing function in the i… - Vidyadip

MCQ

The function $x + {1 \over x},(x \ne 0)$ is a non-increasing function in the interval

✓
$[-1, 1]$
B
$[0, 1]$
C
$[-1, 0]$
D
$[-1,2]$

✓

Answer

Correct option: A.

$[-1, 1]$

a
(a) Let $f(x) = y = x + \frac{1}{x}$

Differentiating with respect to $ x,$ we get

$\frac{{dy}}{{dx}} = f'(x) = 1 - \frac{1}{{{x^2}}} \le 0$

$\, \Rightarrow 1 \le \frac{1}{{{x^2}}}$ or ${x^2} \le 1$

Hence $x \in [ - 1,\,1]$.

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