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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Maxima and Minima

  • question_answer
    The number of values of x where the function \[f(x)=\cos x+\cos (\sqrt{2}x)\] attains its maximum is [IIT 1998; DCE 2001, 05]

    A)            0

    B)            1

    C)            2

    D)            Infinite

    Correct Answer: B

    Solution :

               \[f(x)=\cos x+\cos (\sqrt{2}x)\]                    \[f'(x)=-\sin x-\sqrt{2}\sin (\sqrt{2}x)=0\]                    Hence \[x=0\]is the only solution.                    \[f''(x)=-\cos x-2\cos (\sqrt{2}x)<0\]at \[x=0\]                    Hence maxima occurs at \[x=0\].


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