MCQ
The maximum value of $e^{(2 + \sqrt 3 \cos x + \sin x)}$ is
- A$e^{(2)}$
- B$e^{(2 - \sqrt 3 )}$
- ✓$e^{(4)}$
- D$1$
==> $y' = \exp (2 + \sqrt 3 \cos x + \sin x)\,( - \sqrt 3 \sin x + \cos x)$
Now $y' = 0$ ==> $ - \sqrt 3 \sin x + \cos x = 0$
==> $\sin \left( {x - \frac{\pi }{6}} \right) = 0$ ==> $x = \frac{\pi }{6}$
Now $y''$ is $-ve$ at $x = \frac{\pi }{6}$
Maximum value of
$y = \exp \,\left( {2 + \sqrt 3 \left( {\frac{{\sqrt 3 }}{2}} \right) + \frac{1}{2}} \right)$
$= \exp (4)$.
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where $[x]$ denotes step up function then at $x = 2$ function