A) \[f(x)\] is increasing in \[\left( 0,\frac{\pi }{2} \right)\] and decreasing in \[\left( \frac{\pi }{2},\pi \right)\]
B) \[f(x)\] is decreasing in \[\left( 0,\frac{\pi }{2} \right)\] and increasing in \[\left( \frac{\pi }{2},\pi \right)\]
C) \[f(x)\] is increasing in \[\left( 0,\frac{\pi }{4} \right)\] and decreasing in \[\left( \frac{\pi }{4},\frac{\pi }{2} \right)\]
D) The statements , and are all correct
Correct Answer: C
Solution :
As \[f(x)=\sin 2x\Rightarrow f'(x)=2\cos 2x\] Obviously \[f'(x)>0\]in \[\left( 0,\frac{\pi }{4} \right)\] and \[f'(x)<0\]in \[\left( \frac{\pi }{4},\,\frac{\pi }{2} \right)\] Hence the result.
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