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

  • question_answer
    The tangent drawn at the point (0, 1) on the curve \[y={{e}^{2x}}\] meets x-axis at the point                                      [RPET 2002]

    A)            \[(1/2,\,0)\]

    B)            \[(-1/2,\,\,0)\]

    C)            (2, 0)

    D)            \[(0,\,\,0)\]

    Correct Answer: B

    Solution :

               \[y={{e}^{2x}}\] Þ \[\frac{dy}{dx}=2{{e}^{2x}}\] Þ \[\left( \frac{dy}{dx} \right)_{(0,\,1)}^{{}}=2\]            \ Equation of tangent is, \[y-1=2(x-0)\Rightarrow y=2x+1\]            This tangent meets x-axis, \[\therefore \,\,y=0\]            Þ  \[0=2x+1\Rightarrow x=-1/2\]            \  Co-ordinates of the point \[\left( -\frac{1}{2},\,0 \right)\,\,.\]


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