Applications Of Derivatives Question 399
Question: Consider the function $ f(x)={e^{-2x}} $ sin 2x over the interval $ ( 0,\frac{\pi }{2} ) $ . A real number $ c\in ( 0,\frac{\pi }{2} ),, $ as guaranteed by Rolle-s theorem, such that $ {f}’,(c)=0 $ is
[AMU 1999]
Options:
A) $ \pi /8 $
B) $ \pi /6 $
C) $ \pi /4 $
D) $ \pi /3 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)={e^{-2x}}\sin 2x $
therefore $ {f}’(x)=2{e^{-2x}}(\cos 2x-\sin 2x) $ Now, $ {f}’(c)=0 $
therefore $ \cos 2c-\sin 2c=0 $
therefore $ \tan 2c=1 $
therefore $ c=\frac{\pi }{8} $ .
BETA
