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Manipal Engineering Manipal Engineering Solved Paper-2008

  • question_answer
    The range in which\[y=-{{x}^{2}}+6x-3\]increasing, is

    A) \[x<3\]                

    B) \[x>3\]

    C) \[7<x<8\]           

    D)        \[5<x<6\]

    Correct Answer: A

    Solution :

    Given,\[y=-{{x}^{2}}+6x-3\] \[\Rightarrow \]               \[\frac{dy}{dx}=-2x+6=y\] \[y\]is increasing, if\[y>0\] \[\Rightarrow \]               \[-2x+6>0\]   \[\Rightarrow \]  \[-2x>-6\] \[\Rightarrow \]               \[2x<6\]           \[\Rightarrow \]  \[x<3\]  


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