Applications Of Derivatives Question 241
Question: Which one is the correct statement about the function $ f(x)=\sin 2x $
Options:
A) $ f(x) $ is increasing in $ ( 0,\frac{\pi }{2} ) $ and decreasing in $ ( \frac{\pi }{2},\pi ) $
B) $ f(x) $ is decreasing in $ ( 0,\frac{\pi }{2} ) $ and increasing in $ ( \frac{\pi }{2},\pi ) $
C) $ f(x) $ is increasing in $ ( 0,\frac{\pi }{4} ) $ and decreasing in $ ( \frac{\pi }{4},\frac{\pi }{2} ) $
D) The statements , and are all correct
Show Answer
Answer:
Correct Answer: C
Solution:
As $ f(x)=\sin 2x\Rightarrow f’(x)=2\cos 2x $ Obviously $ f’(x)>0 $ in $ ( 0,\frac{\pi }{4} ) $ and $ f’(x)<0 $ in $ ( \frac{\pi }{4},,\frac{\pi }{2} ) $
Hence the result.
BETA
