Applications Of Derivatives Question 259
Question: If $ f(x)=\sin x-\cos x, $ the function decreasing in $ 0\le x\le 2\pi $ is
[UPSEAT 2001]
Options:
A) $ [5\pi /6,,3\pi /4] $
B) $ [\pi /4,,\pi /2] $
C) $ [3\pi /2,,5\pi /2] $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=\sin x-\cos x $
$ {f}’(x)=\cos x+\sin x=\sqrt{2}[ \cos ( x-\frac{\pi }{4} ) ] $ = $ \sqrt{2}\cos ( x-\frac{\pi }{4} ) $
For $ f(x) $ decreasing, $ {f}’(x)<0 $
$ \frac{\pi }{2}<( x-\frac{\pi }{4} )<\frac{3\pi }{2} $ , (within $ 0\le x\le 2\pi $ ).
therefore $ \frac{3\pi }{4}<x\le \frac{7\pi }{4} $ .
BETA
