question_answer

If p > 2 then the. maximum value of the function \[f\,(x)=\cos 2x+2p\sin x\]is:

A) \[2p-3\]

B) \[-\,1\]

C) \[-\,3-2p\]

D) \[-1+2p\]

Correct Answer: D

Solution :

\[f'\,(x)=-\,2\sin 2x+2p\,\cos x\]

\[f'\,(x)=-\,2\cos x\,(2\sin x-p)\]

Since \[p>2\]\[\Rightarrow \]\[2\sin x-p<0\]

Hence \[f'\,(x)\]will have same sigh as \[\cos \,\,x\]

Hence maximum value is at \[x=\pi /2\] which is equal to \[-1+2p\]