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

  • question_answer
    If the length of sub-normal is equal to the length of sub-tangent at my point (3, 4) on the curve y=f(x) and the tangent at (3, 4) to y=f(x) meets the coordinate axes at A and B, then the maximum area of the triangle OAB, where O is origin, is

    A) 45/2                 

    B) 49/2

    C) 25/2                 

    D) 81/2            

    Correct Answer: B

    Solution :

    [b] Length of sub-normal = length of the sub-tangent or \[\frac{dy}{dx}=\pm 1\] If \[\frac{dy}{dx}=1\], equation of the tangent is \[y-4=x-3\] or \[y-x=1\] area of \[\Delta OAB=\frac{1}{2}\times 1\times 1=\frac{1}{2}\] If \[\frac{dy}{dx}=-1,\]equation of the tangent is \[y-4=-x+3\] Or \[y+x=7,\] Area \[=\frac{1}{2}\times 7\times 7=\frac{49}{2}\]


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