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STD 12 - 6. Application of derivatives — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 6. Application of derivatives4 Marks
MCQ
In which interval $f(x) = 2x^2 - \ln |x| ,$  $(x \ne 0)$ is monotonically decreasing -
  • A
    $(-1/2 , 1/2)$
  • B
    $(- \infty , -1/2)$
  • ✓
    $( - \infty , - 1/2)\, \cup \,(0,1/2)$
  • D
    $( - \infty , - 1/2)\, \cup \,(1/2,\,\infty )$
✓

Answer

Correct option: C.
$( - \infty , - 1/2)\, \cup \,(0,1/2)$
c
$f(x)=2 x^{2}-\ln |x|$

$f^{1}(x)=4 x-\frac{1}{x}<0$

$\Longrightarrow x\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)<0 \Longrightarrow x \in\left(-\infty,-\frac{1}{2}\right) \cup\left(0, \frac{1}{2}\right)$

$\ln (2), f(x)$ is monotonically decreasing

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