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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        What is the value of b for which\[f(x)=\sin x-bx+c\] is decreasing in the interval\[(-\infty ,\infty )\]?

    A)  \[b<1\]                               

    B)  \[b\ge 1\]

    C)  \[b>1\]                               

    D)  \[b\le 1\]

    Correct Answer: C

    Solution :

                    Given, \[f(x)=\sin x-bx+c\] \[\Rightarrow \]               \[f(x)=\cos x-b\] Since, it is decreasing, \[\therefore \]  \[f(x)<0\] \[\Rightarrow \]               \[\cos x<b\] \[\Rightarrow \]               \[b>1\]                                 \[(\because \cos x\le 1)\]


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