KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • 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 \[-1+2p\]

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