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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


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

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

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

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