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

  • question_answer
    The function \[y=a(1-\cos x)\] is maximum when \[x=\]                                                                                   [Kerala (Engg.) 2002]

    A)            \[\pi \]

    B)            \[\pi /2\]

    C)            \[-\pi /2\]

    D)            \[-\pi /6\]

    Correct Answer: A

    Solution :

               \[y=a\,(1-\cos x)\]Þ\[{y}'=a\sin x\]                    Þ \[{y}'=0\Rightarrow \sin x=0\] Þ \[x=0,\,\pi \]            Now \[{y}''=a\cos x\] Þ \[{y}''(0)=a\] and \[{y}''(\pi )=-a\]            Hence y is maximum when \[x=\pi \].


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