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Math Help - Cubic equation

  1. #1
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    Cubic equation

    I've been stuck on this problem for a while, after starting C1 AS level maths a few weeks ago. Here is the question:

    Curve C => y = ax - x + x - 5, a is some constant.
    Point P => (-1/2, y)
    Tangent to C at P is parallel to y = (7x - 1)/2

    Find a.

    Any help will be appreciated, thanks.
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Cubic equation

    Quote Originally Posted by b150 View Post
    I've been stuck on this problem for a while, after starting C1 AS level maths a few weeks ago. Here is the question:

    Curve C => y = ax - x + x - 5, a is some constant.
    Point P => (-1/2, y)
    Tangent to C at P is parallel to y = (7x - 1)/2

    Find a.

    Any help will be appreciated, thanks.
    Parellel to y = (7/2)x - 1/2 means the slope of the tangent (at x = -1/2) is 7/2
    So if f(x) = ax^3 -x^2 + x - 5, then f ' (-1/2) = ...

    Can you take it from here?
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: Cubic equation

    Quote Originally Posted by b150 View Post
    I've been stuck on this problem for a while, after starting C1 AS level maths a few weeks ago. Here is the question:

    Curve C => y = ax - x + x - 5, a is some constant.
    Point P => (-1/2, y)
    Tangent to C at P is parallel to y = (7x - 1)/2

    Find a.

    Any help will be appreciated, thanks.
    The tangent of C is f'\left(-\dfrac{1}{2}\right) and since parallel lines have the same gradient f'\left(-\dfrac{1}{2}\right) = \dfrac{7}{2}

    Solve for a


    edit: too slow
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  4. #4
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    Clarksville, ARk
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    Re: Cubic equation

    This looks like a calculus question.

    Do you know how to find the derivative of this cubic function?

    Do you know what a derivative tells about a function?
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  5. #5
    Super Member TheChaz's Avatar
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    Re: Cubic equation

    Quote Originally Posted by e^(i*pi) View Post
    ...


    edit: too slow
    ...but much better looking!
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  6. #6
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    Re: Cubic equation

    haha I realised how to do it like 5 minutes after I posted :P Thanks anyway.
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  7. #7
    Senior Member
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    Re: Cubic equation

    Quote Originally Posted by TheChaz View Post
    ...but much better looking!
    I don't see how you can say that e^(i*pi) is much better looking ! He doesn't even show a picture of himself.

    ... Oh! You mean his post was much better looking? Yes, it does look good -- LaTeX does that.
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