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Find parameter p so that y = 3x is a tangent line to the curve y = x 2 + p

Find parameter p so that y = 3x is a tangent line to the curve
y = x 2 + p

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear nitin,

  • The slope of the tangent is equal to 3. At the point of tangency y ' = 3.

    y ' = 2 x = 3

  • Solve the equation 2 x = 3 to find the x coordinate of the point of tangency.

    x = 3 / 2

  • The point of tangency is on the line y = 3 x, therefore the y coordinate of the point of tangency is equal to

    y = 3 (3/2) = 9 / 2

  • The point of tangency (3 / 2 , 9 / 2) is on the curve
    y = x 2 + p and is therefore used to find p as follows

    9 / 2 = (3 / 2) 2 + p

  • Solve the above for p to obtain

    p = 9 / 4

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