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    Find the coordinates of any stationary points on these curves and state, giving reasons whether the points are maximum, minimum or points of inflexion.

     y=x^{4}+3x^{3}

     \frac{\mathrm{d} y}{\mathrm{d} x} = 4x^{3}+9x^{2}
    put dy/dx = 0

     x(4x^{2}+9x)=0

 x=0 or 4x^{2}+9x=0
    but doesn't  4x^{2}+9x=0 has no real roots

    but in the book the answer was (0,0) is inflexion which is right

    but it also gave this answer  (-\frac{9}{3}, -\frac{2187}{256}) is a min

    how did the book get the second answer

    Please help
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    take a factor of x^2 out instead of x from your dy/dx
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    (Original post by bigmansouf)
    Question
    Find the coordinates of any stationary points on these curves and state, giving reasons whether the points are maximum, minimum or points of inflexion.

     y=x^{4}+3x^{3}

     \frac{\mathrm{d} y}{\mathrm{d} x} = 4x^{3}+9x^{2}
    put dy/dx = 0

     x(4x^{2}+9x)=0

 x=0 or 4x^{2}+9x=0
    but doesn't  4x^{2}+9x=0 has no real roots

    but in the book the answer was (0,0) is inflexion which is right

    but it also gave this answer  (-\frac{9}{3}, -\frac{2187}{256}) is a min

    how did the book get the second answer

    Please help

    I think you mean -9/4, as -9/3 is just -3. That's your first hint.

    The second - just like you got x = 0, can you factorise the polynomial you say has no real roots? Or better yet, go back and do this in one step instead of two?
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    (4x^2+9x) = 0
    x(4x+9) = 0
    x = -9/4
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    (Original post by SeanFM)
    I think you mean -9/4, as -9/3 is just -3. That's your first hint.

    The second - just like you got x = 0, can you factorise the polynomial you say has no real roots? Or better yet, go back and do this in one step instead of two?
    woow thanks
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    (Original post by Razzamataz179)
    (4x^2+9x) = 0
    x(4x+9) = 0
    x = -9/4
    thanks im rushing tonight to finish differentiation
    i didnt seee my own mistakes
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    Cool, I remember doing this sort of question in the FSMQ Additional maths Good old dy/dx
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    (Original post by bigmansouf)
    thanks im rushing tonight to finish differentiation
    i didnt seee my own mistakes
    What year are you in?
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    (Original post by SCAR H)
    What year are you in?
    im just doing it for myself i want to do computer science in uni
    i changed my career
    i didnt want to do economics any more
 
 
 
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