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    http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf


    For question 7d how do I know the graph is U shaped, exam solutions said its U shaped, but how do I know that. This doesnt look quadratic either.

    Thank you
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    Graphs of functions to the fourth degree are u-shaped, and you can see that it is to the fourth power. I think you're just supposed to recognise that it would be U-shaped somewhat
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    (Original post by JustgotAstar)
    http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf


    For question 7d how do I know the graph is U shaped, exam solutions said its U shaped, but how do I know that. This doesnt look quadratic either.

    Thank you
    Any even order polynomial will be ultimately 'U' shaped.
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    (Original post by RDKGames)
    Any even order polynomial will be ultimately 'U' shaped.
    Only if it's biquadratic, right ? So can be expressed in terms of a quadratic.
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    (Original post by NotNotBatman)
    Only if it's biquadratic, right ? So can be expressed in terms of a quadratic.
    Doesn't have to be.
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    (Original post by NotNotBatman)
    Only if it's biquadratic, right ? So can be expressed in terms of a quadratic.
    A very strangely shaped U perhaps (might be closer to a v/w), but a rough U shape nonetheless.
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    You have to use he fact that it has one turning point and the fact that it is a polynomial of even degree - which shows  f(x)\rightarrow \infty as  x\rightarrow \pm \infty (as coefficient of x^4 is positive anyway).
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    (Original post by RDKGames)
    Doesn't have to be.
    Ok.

    (Original post by _gcx)
    A very strangely shaped U perhaps (might be closer to a v), but a rough U shape nonetheless.
    I was thinking more of the w shaped curves, when the coefficients of each x^n is non zero and there's more than one stationary point.
    B9710 has explained it really well.
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    So say I have x to the power 6, it would be U shaped? Wouldnt the amount of turning points change at all? Would all even powers have 1 turning point then?
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    (Original post by JustgotAstar)
    So say I have x to the power 6, it would be U shaped? Wouldnt the amount of turning points change at all? Would all even powers have 1 turning point then?
    It is 'ultimately' U shaped, yes, because an even order polynomial goes to infinity as x \rightarrow \pm \infty. Anything can happen in between the two stems to infinity, you need further analysis of the stationary points to determine what happens there.

    All even powers at at least 1 turning point.
 
 
 
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