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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
If $f(x) = \sin x - \cos x,$ the function decreasing in $0 \le x \le 2\pi $ is
  • A
    $[5\pi /6,\,3\pi /4]$
  • B
    $[\pi /4,\,\pi /2]$
  • C
    $[3\pi /2,\,5\pi /2]$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d) $f(x) = \sin x - \cos x$

$f'(x) = \cos x + \sin x = \sqrt 2 \left[ {\cos \,\,\left( {x - \frac{\pi }{4}} \right)} \right]$

$=\sqrt 2 \cos \left( {x - \frac{\pi }{4}} \right)$

For $f(x)$ decreasing, $f'(x) < 0$

$\frac{\pi }{2} < \left( {x - \frac{\pi }{4}} \right) < \frac{{3\pi }}{2}$, (within $0 \le x \le 2\pi $).

==> $\frac{{3\pi }}{4} < x \le \frac{{7\pi }}{4}$.

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