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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Increasing and Decreasing Function

  • question_answer
    If the function \[f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x}\]is increasing for all values of x, then

    A)            \[K<1\]

    B)            \[K>1\]                                   

    C)            \[K<2\]

    D)            \[K>2\]

    Correct Answer: D

    Solution :

               Since \[f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x}\]is increasing for all x, therefore \[f'(x)>0\]for all x                    \[\Rightarrow \frac{K-2}{{{(\sin x+\cos x)}^{2}}}>0\]for all x                    Þ\[K-2>0\Rightarrow K>2\].


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