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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Mock Test - Application of Derivatives

  • question_answer
    The equation of the tangent to the curve \[y=b{{e}^{-x/a}}\] at the point where it crosses the y-axis is

    A) \[\frac{x}{a}-\frac{y}{b}=1\]

    B) \[ax+by=1\]

    C) \[ax-by=1\]       

    D) \[\frac{x}{a}+\frac{y}{b}=1\]

    Correct Answer: D

    Solution :

    [d] \[y=b{{e}^{-x/a}}\]meets the y-axis at (0, b). Again, \[y=b{{e}^{-x/a}}\left( -\frac{1}{a} \right)\] \[At(0,b),\frac{dy}{dx}=b{{e}^{0}}\left( -\frac{1}{a} \right)=-\frac{b}{a}\] Therefore, required tangent is \[y-b=-\frac{b}{a}(x-0)\] or \[\frac{x}{a}+\frac{y}{b}=1\]


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