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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
The minimum value of the function $2\cos 2x - \cos 4x$ in $0 \le x \le \pi $ is
  • A
    $0$
  • B
    $1$
  • C
    ${3 \over 2}$
  • ✓
    $-3$
✓

Answer

Correct option: D.
$-3$
d
(d) $y = 2\cos 2x - \cos 4x$

$ = 2\cos 2x(1 - \cos 2x) + 1 = 4\cos 2x{\sin ^2}x + 1$

Obviously, ${\sin ^2}x \ge 0$

Therefore to be least value of $y,$ $\cos 2x$ should be least $i.e.,$ $ - 1$.

Hence least value of $y$  is $ - \,4 + 1 = - 3$.

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