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KVPY Sample Paper KVPY Stream-SX Model Paper-24

  • question_answer
    If a < 0, \[f(x)={{e}^{ax}}+{{e}^{-ax}}\] and S := {x; f(x) is monotonically decreasing}, then S equals

    A) \[\{x:x>0\}\]

    B) \[\{x:x<0\}\]

    C) \[\{x:x>1\}\]

    D) \[\{x:x<1\}\]

    Correct Answer: B

    Solution :

    \[f'(x)=a\,\,({{e}^{ax}}-{{e}^{-\,ax}})<0\]\[\Rightarrow {{e}^{ax}}>{{e}^{-\,ax}}\]\[(\because a<0)\] \[\Rightarrow x<0\]   


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