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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    The set of all values of the parameter 'a' for which the function; \[f(x)=8ax-a\text{ }\sin \text{ }6x-7x-\sin \text{ }5x\] increases & has no critical points for all \[x\in R\], is

    A) [-1, 1]

    B) \[(-\infty ,-6)\]

    C) \[(6,+\infty )\]

    D) \[[6,+\infty )\]   

    Correct Answer: D

    Solution :

    \[f(x)=8ax-a\sin 6x-7x-\sin 5x\]
    \[f'(x)=8a-6a\cos 6x-7-5\cos 5x=8a-7\]\[-6a\cos 6x-5\cos 5x\]
    f (x) is an increasing function
    \[f'(x)\ge 0\]       
    \[\therefore \]      \[8a-7\ge 6a+5\]\[\Rightarrow \]\[2a\ge 12\,\,;\,\,a\ge 6\,\,;\,\,a\in [6,\infty )\]


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