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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Tangent and Normal

  • question_answer
    If a tangent to the curve \[y=6x-{{x}^{2}}\]is parallel to the line \[4x-2y-1=0\], then the point of tangency on the curve is                                                               [Karnataka CET 2004]

    A)            (2, 8)

    B)            (8, 2)

    C)            (6, 1)

    D)            (4, 2)

    Correct Answer: A

    Solution :

               Given \[y=6x-{{x}^{2}}\]                                                    .....(i)                       \[\frac{dy}{dx}=6-2x\]                    Since, tangent is parallel to the line x\[4x-2y-1=0\]                    \ \[\frac{dy}{dx}=6-2x=\frac{-4}{-2}\Rightarrow 6-2x=2\Rightarrow x=2\]                    Put the value of x in (i), we get \[y=8\]            Hence required point of tangency will be \[(2,\,8)\].


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