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Math Help - finding k so line is tangent to graph

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    finding k so line is tangent to graph

    Find k such that the line is tangent to the graph of the function



    don't know how to do this one
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  2. #2
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    Quote Originally Posted by Neverending View Post
    Find k such that the line is tangent to the graph of the function



    don't know how to do this one
    At what value of x does the line need to be tangent to the function?
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    Quote Originally Posted by Neverending View Post
    Find k such that the line is tangent to the graph of the function



    don't know how to do this one
    A non-calculus approach is to solve them simultanously for x and set the discriminant of the resulting quadratic equation equal to zero (so that there's only one intersection point):

    x^2 - kx = 4x - 9 \, ...
    Last edited by mr fantastic; January 12th 2009 at 02:07 AM. Reason: Claculus --> calculus
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    Quote Originally Posted by Prove It View Post
    At what value of x does the line need to be tangent to the function?
    I think it wants all values of x where it would be tangent. It must have to do with the derivative because that's the chapter im on. I just don't know what to do with it.

    well the deriv = 2x - k

    Am I suppose to set that equal to the slope perhaps?? but when I do I get something like 2x-4... what to do with that?
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    Quote Originally Posted by mr fantastic View Post
    A non-calculus approach is to solve them simultanously for x and set the discriminant of the resulting quadratic equation equal to zero (so that there's only one intersection point):

    x^2 - kx = 4x - 9 \, ...
    \Rightarrow x^2 - (k+4)x + 9 = 0.

    Discriminant: \Delta = (k+4)^2 - 36.

    Solve \Delta = 0: k + 4 = \pm 6 \Rightarrow k = -10, \, 2.


    Calculus approach:

    Gradient of tangent = 4 therefore require \frac{dy}{dx} = 4:

    2x - k = 4 .... (1)

    At the point of tangency require the y-coordinate to be the same for the tangent line and the curve:

    x^2 - kx = 4x - 9 \Rightarrow x^2 - (k + 4)x + 9 = 0 .... (2)

    Solve equations (1) and (2) simultaneously for k: k = -10, \, 2.
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  6. #6
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    yay I got it! Thanks so much
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