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

  • question_answer
    The abscissae of the points, where the tangent to curve \[y={{x}^{3}}-3{{x}^{2}}-9x+5\]is parallel to x-axis, are                    [Karnataka CET 2001]

    A)            0 and 0

    B)            x = 1 and ? 1

    C)            x = 1 and ? 3

    D)            x =  ? 1 and 3

    Correct Answer: D

    Solution :

               \[y={{x}^{3}}-3{{x}^{2}}-9x+5\] Þ \[\frac{dy}{dx}=3{{x}^{2}}-6x-9.\]            We know that this equation gives the slope of the tangent to the curve. The tangent is to parallel to x-axis, \[\therefore \]\[\frac{dy}{dx}=0\]. Therefore \[3{{x}^{2}}-6x-9=0\]   Þ \[x=-1,\,3\].


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