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Math Help - Tangent to a curve; constant k

  1. #1
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    Tangent to a curve; constant k

    Hi guys,

    I am confused with this one. Would I still use dy/dx? If not, could someone please provide me with a formula?

    Find the value of the constant k for which the line y + 2x = k is a tangent to the curve y = x - 6x + 14

    Thanks
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  2. #2
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    Quote Originally Posted by laoch View Post
    Hi guys,

    I am confused with this one. Would I still use dy/dx? If not, could someone please provide me with a formula?

    Find the value of the constant k for which the line y + 2x = k is a tangent to the curve y = x - 6x + 14

    Thanks
    The simplest approach is to solve for the intersection points of the line and parabola and then force the value of k to be such that there's only one intersection point:

    y + 2x = k \Rightarrow y = k - 2x .... (1)

    y = x^2 - 6x + 14 .... (2)

    Start solving equations (1) and (2) simultaneously:

    k - 2x = x^2 - 6x + 14 \Rightarrow x^2 - 4x + (14 + k) = 0.

    There will be only one solution (and hence y + 2x = k will be a tangent to y = x^2 - 6x + 14) if the discriminant of this quadratic is equal to zero:

    (-4)^2 - 4(1)(14 + k) = 0 \Rightarrow k = \, ....
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  3. #3
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    Thank you so much
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