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J & K CET Engineering J and K - CET Engineering Solved Paper-2011

  • question_answer
    If  \[f(x)\,=kx\,-\,\cos \,x\] is   monotonically increasing for all \[x\in R,\] then

    A)  \[k>-1\]          

    B)  \[k>-1\]

    C)  \[k>1\]            

    D)  None of these

    Correct Answer: A

    Solution :

    Given,  \[f(x)=kx-\cos x\] and \[x\in R\] \[f'(x)=k+\sin x\] Since, the function \[f(x)\] is monotonically increase for all \[x\in R\]. \[\therefore \] \[f'(x)>0,\,\,\,\forall \,\,\,\,x\in R\] \[\Rightarrow \] \[f'\left( \frac{\pi }{2} \right)>0\] \[\Rightarrow \] \[k+\sin \frac{\pi }{2}>0\] \[\Rightarrow \] \[k+1>0\] \[\Rightarrow \] \[k>-1\]


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