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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
The function $f(x) = \cos x - 2px$ is monotonically decreasing for
  • A
    $p < {1 \over 2}$
  • ✓
    $p > {1 \over 2}$
  • C
    $p < 2$
  • D
    $p > 2$
✓

Answer

Correct option: B.
$p > {1 \over 2}$
b
(b) $f(x)$ will be monotonically decreasing, if $f'(x) < 0$.

==> $f'(x) = - \sin x - 2p < 0$ ==>$\frac{1}{2}\sin x + p > 0$

==> $p>\frac{1}{2}\,,\,\,[\because -1\le \sin x\le 1]$

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