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    Question 6:


    \mathrm{The\ curve} C \mathrm{has\ equation}


    y = 4 \sqrt x^5\ - 1\ , \ x\geq 0


    \mathrm{Show\ clearly\ that}

    4x^2 \frac{d^2 y}{d x^2}\ -15\ y=k

    \mathrm{Where} k \mathrm{is\ an\ integer\ to\ be\ found}

    I've never covered this so I'm unsure what the interaction is when \frac{d^2 y}{d x^2} Is part of the equation. Or even how to approach this.

    Anyway I've done the easy part: \frac{d^2 y}{d x^2}\ =\ 15x^{1/2}
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    (Original post by 34908seikj)
    Question 6:


    \mathrm{The\ curve} C \mathrm{has\ equation}


    y = 4 \sqrt x^5\ - 1\ , \ x\geq 0


    \mathrm{Show\ clearly\ that}

    4x^2 \frac{d^2 y}{d x^2}\ -15\ y=k

    \mathrm{Where} k \mathrm{is\ an\ integer\ to\ be\ found}

    I've never covered this so I'm unsure what the interaction is when \frac{d^2 y}{d x^2} Is part of the equation. Or even how to approach this.

    Anyway I've done the easy part: \frac{d^2 y}{d x^2}\ =\ 15x^{1/2}
    There isn't anything that is beyond C1 here.

    The question is just asking you to show that the equation is true where k is an integer.

    So multiply \frac{d^2 y}{d x^2} by 4x^2 then subtract 15y and you should end up with an integer once you've simplified.

    EDIT : If you've written the question correctly then your \frac{d^2 y}{d x^2} is wrong.
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    If that \sqrt{x}^5 is meant to mean x^{\frac{5}{2}} then your \frac{d^2y}{dx^2} seems correct. Once you multiply that by 4x^2 you are left with 60x^{5/2}.

    Now subtract 15y = 15(4 \cdot x^{5/2} - 1) = 60x^{\frac{5}{2}} - 15 away from that, what integer are you left with?
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    (Original post by Zacken)
    If that \sqrt{x}^5 is meant to mean x^{\frac{5}{2}} then your \frac{d^2y}{dx^2} seems correct. Once you multiply that by 4x^2 you are left with 60x^{5/2}.

    Now subtract 15y = 15(4 \cdot x^{5/2} - 1) = 60x^{\frac{5}{2}} - 15 away from that, what integer are you left with?
    Ah, so It would just be 15, K=15.

    Since this is obviously not C1, would this be covered in C2. If not what unit?
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    (Original post by 34908seikj)
    Ah, so It would just be 15, K=15.

    Since this is obviously not C1, would this be covered in C2. If not what unit?
    Yeah, sounds about right.

    idk, looks like standard C1 to me.
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    (Original post by 34908seikj)
    Ah, so It would just be 15, K=15.

    Since this is obviously not C1, would this be covered in C2. If not what unit?
    Ignore what I said about your \frac{d^2y}{dx^2} being wrong.

    This is a C1 question. Maybe the question is a bit different to something that you would see in e.g. an Edexcel paper.

    What about it makes you think it's beyond C1?
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    (Original post by notnek)
    Ignore what I said about your \frac{d^2y}{dx^2} being wrong.

    This is a C1 question. Maybe the question is a bit different to something that you would see in e.g. an Edexcel paper.

    What about it makes you think it's beyond C1?
    Maybe it just uses concepts from C1, just on steroids.

    I've done every official Edexcel C1 exam paper, and I've never come across a question like this.


    The most you do with \frac{d^2y}{dx^2}is literally just differentiating a second time, that's it.
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    (Original post by 34908seikj)
    Maybe it just uses concepts from C1, just on steroids.

    I've done every official Edexcel C1 exam paper, and I've never come across a question like this.


    The most you do with \frac{d^2y}{dx^2}is literally just differentiating a second time, that's it.
    It's not on steroids, it is a fairly simple application, just somewhat unusual for Edexcel. It is good to look at IYGB because its slightly offbeat questions like this one are still entirely on the Edexcel syllabus and might be similar to the sort of thing Edexcel sometimes throw in to differentiate (not in the maths way..) at the top level.
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    (Original post by 13 1 20 8 42)
    It's not on steroids, it is a fairly simple application, just somewhat unusual for Edexcel. It is good to look at IYGB because its slightly offbeat questions like this one are still entirely on the Edexcel syllabus and might be similar to the sort of thing Edexcel sometimes throw in to differentiate (not in the maths way..) at the top level.
    Yup, completely agree. I've learnt some really neat things from doing I.Y.G.B papers.
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    (Original post by 34908seikj)
    Maybe it just uses concepts from C1, just on steroids.
    No, it is a simple and standard concept from C1. This would have been a very easy GCSE question for me.
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    (Original post by Zacken)
    No, it is a simple and standard concept from C1. This would have been a very easy GCSE question for me.
    Well that's good for you & I'm sorry I'm not as "good" at maths as you were when you were doing GCSEs/ AS's.


    It's clearly not a standard C1 concept, at least on an Edexcel paper, given by the fact I've never seen that type of question before. That said no need to be so aggressive man :/
 
 
 
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