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nitin singh Grade: 12
        


Find p and q so that y = 2 x is a tangent, line at x = 3, to the curve
y = p x 2 + q x + 2

7 years ago

Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear nitin,




  • The point of tangency is on the tangent line y = 2x, hence its y coordinate can also be calculated and its coordinates given by

    (3 , 2(3)) = (3 , 6)


  • The above point of tangency is also on the curve
    y = p x 2 + q x + 2, hence


    6 = p(3) 2 + q (3) + 2


  • Let us now find y '

    y ' = 2 p x + q


  • At x = 3 y ' is equal to the slope of the tangent line y = 2 x. Hence

    2 = 2 p (3) + q


  • We now solve the two linear equations

    9 p + 3 q = 4 and 6 p + q = 2


  • to find 9 p + 3 q = 4 and 6 p + q = 2

    p = 2 / 9 and q = 2 / 3






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Sagar Singh


B.Tech IIT Delhi







7 years ago
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