The function $2 x^{2} - log x$ is a decreasing function if $x$ belongs to the interval

(- \frac{1}{2}, \frac{1}{2})

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(- \frac{1}{2}, 0)

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(0, \frac{1}{2})

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(- 2, 2)

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Solution

The correct option is C $(0, \frac{1}{2})$
$f^{'} (x) = 4 x - \frac{1}{x}$
$f^{'} (x) = \frac{(4 x^{2} - 1)}{x}$
$f^{'} (x) < 0$ when $x \in (0, \frac{1}{2})$

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