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Math Help - Slope of Tangent Intersecting with Line

  1. #1
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    Slope of Tangent Intersecting with Line

    Determine the slope of the tangent to y=x^2+9x+9 at the point where the curve intersects the line y=3x.


    The answer in the textbook is just 3. Why is this so? I don't know how they got this.

    The slope of the LINE is 3. But don't I have to find the slope of the tangent? in which case I find the derivative?

    I did this:

    y'=2x+9
    but then how did they get 3?
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  2. #2
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    Quote Originally Posted by john-1 View Post
    Determine the slope of the tangent to y=x^2+9x+9 at the point where the curve intersects the line y=3x.


    The answer in the textbook is just 3. Why is this so? I don't know how they got this.

    The slope of the LINE is 3. But don't I have to find the slope of the tangent? in which case I find the derivative?

    I did this:

    y'=2x+9
    but then how did they get 3?
    first, find the point(s) of intersection ...

    x^2+9x+9 = 3x

    x^2+6x+9 = 0

    (x+3)^2 = 0

    x = -3

    slope of the curve is y' = 2x+9 ... at the point of intersection, the slope of the curve is ...

    y'(-3) = 2(-3)+9 = 3
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