Applications Of Derivatives Question 236
Question: The maximum value of exp $ (2+\sqrt{3}\cos x+\sin x) $ is
[AMU 1999]
Options:
A) $ \exp (2) $
B) $ \exp (2-\sqrt{3}) $
C) $ \exp (4) $
D) 1
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ y=\exp (2+\sqrt{3}\cos x+\sin x) $
therefore $ {y}’=\exp (2+\sqrt{3}\cos x+\sin x),(-\sqrt{3}\sin x+\cos x) $
Now $ {y}’=0 $
therefore $ -\sqrt{3}\sin x+\cos x=0 $
therefore $ \sin ( x-\frac{\pi }{6} )=0 $
therefore $ x=\frac{\pi }{6} $
Now $ {y}’’ $ is -ve at $ x=\frac{\pi }{6} $
\Maximum value of
$ y=\exp ,( 2+\sqrt{3}( \frac{\sqrt{3}}{2} )+\frac{1}{2} ) $ = $ \exp (4) $ .
BETA
