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Math Help - calculus

  1. #1
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    calculus

    I seen a question on a practice paper a while back which confused me a 'lil. Here it is:
    Source: [6663]Edexcel GCE Core Mathematics C1 AS - Monday 10th Januaryy 2005


    Question 9


    The gradient of the curve C is given by
    \frac{dy}{dx}<br />
=(3x-1)^2


    The point P(1,4) lies on C. (For reference, but was used for questions A and B)


    c) Using dy/dx, show that there is no point on C at which the tangent is parallel to the line
    y=1-2x


    I don't know where to start on this question, so any help would be great :x, especially since I have a C1 exam in ~ 2 hours. D:

    So far, all I know is that the gradient of y=1-2x is obviously -2 and the increment (+1) doesn't matter (hence, parallel).
    (3x-1)^2=9x^2-6x+1
    So those are the 2 gradients of the equasion, and I have no idea on how to show that there's no point on C where they're parallel.
    Last edited by Bladescope; January 8th 2009 at 11:48 PM. Reason: Wrapping the formulae in [MATH] tags.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Bladescope View Post
    I seen a question on a practice paper a while back which confused me a 'lil. Here it is:
    Source: [6663]Edexcel GCE Core Mathematics C1 AS - Monday 10th Januaryy 2005


    Question 9


    The gradient of the curve C is given by
    \frac{dy}{dx}<br />
=(3x-1)^2


    The point P(1,4) lies on C. (For reference, but was used for questions A and B)


    c) Using dy/dx, show that there is no point on C at which the tangent is parallel to the line
    y=1-2x


    I don't know where to start on this question, so any help would be great :x, especially since I have a C1 exam in ~ 2 hours. D:

    So far, all I know is that the gradient of y=1-2x is obviously -2 and the increment (+1) doesn't matter (hence, parallel).
    (3x-1)^2=9x^2-6x+1
    So those are the 2 gradients of the equasion, and I have no idea on how to show that there's no point on C where they're parallel.
    parallel means they have the same slope. so you need to show that dy/dx = -2 is never true.

    this should be somewhat obvious. dy/dx is a square, and is thus greater than or equal to zero for all x, while -2 < 0. they cannot be equal

    thus, dy/dx never matches the slope of the line in question and so there is no tangent line that is parallel to the said line
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