Which one of the following is correct in respect of the function f(x) = x sin x + cos x + $\frac{1}{2}$ cos2 x?

Question

Which one of the following is correct in respect of the function f(x) = x sin x + cos x + $\frac{1}{2}$ cos2 x?

TuteeHUB · Accepted Answer

It remains constant in the interval $\left( {0\frac{\pi }{2}} \right)$

TuteeHUB · Answer

It is increasing in the interval $\left( {0,\frac{\pi }{2}} \right)$

TuteeHUB · Answer

it is decreasing in the interval $\left( {0,\frac{\pi }{2}} \right)$

TuteeHUB · Answer

It is decreasing in the interval $\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$

1.	Which one of the following is correct in respect of the function f(x) = x sin x + cos x + \(\frac{1}{2}\) cos2 x?
A.	It is increasing in the interval \(\left( {0,\frac{\pi }{2}} \right)\)
B.	It remains constant in the interval \(\left( {0\frac{\pi }{2}} \right)\)
C.	it is decreasing in the interval \(\left( {0,\frac{\pi }{2}} \right)\)
D.	It is decreasing in the interval \(\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)\)
Answer» B. It remains constant in the interval \(\left( {0\frac{\pi }{2}} \right)\)

Which one of the following is correct in respect of the function f(x) = x sin x + cos x + \(\frac{1}{2}\) cos2 x?