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    I was doing question 9 in the Edexcel C2 specimen paper and it was all going well until they told me to differentiate this...

    A=1/4(x^3-7x^2+8x+16) where A is the area of a triangle, and the question is asking to prove that A is a maximum when x=2/3

    In the solution it says "ignore the 1/4", which ive done and it comes out fine, but I don’t understand why ive been able to ignore it. And also in the solutions when they prove that its a maximum they put the 1/4 back and say

    D2A/DX2=1/4(6x-14), which is <O so is a maximum.

    Which confused me more

    I think I should go to bed now cos its 11.29

    Thanks a lot

    Rob
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    It's basically becauase you know you'll be setting dA/dx to zero.

    So think of writing 4A = ...

    Then 4dA/dx = ....

    0 = ....

    They're just putting the factor back afterwards to be a bit rigorous. Although we can see that it won't affect the answer in this case it might have been a negative factor for example, which would have meant disregarding it in the first part was still valid but putting it back in the second part is crucial.
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    (Original post by bertus)
    I was doing question 9 in the Edexcel C2 specimen paper and it was all going well until they told me to differentiate this...

    A=1/4(x^3-7x^2+8x+16) where A is the area of a triangle, and the question is asking to prove that A is a maximum when x=2/3

    Rob
    A = (4x^3-28x^2+32x+64)^-1
    dA/dx = (-(4x^3-28x^2+32x+64)^-2) x (12x^2-56x+32)
    (12x^2-56x+32)(-4x^3+28x^2-32x-64)^-2

    Turning points at dA/dx = 0
    (12x^2-56x+32)(-4x^3+28x^2-32x-64)^-2 = 0

    In the above equation just substitute x = 2/3
    If the equation gives 0, then you know that point A (x = 2/3) is a turning point, as you substitute you'll see that the first bracket gives 0, hence this equation is 0.

    To prove the turning point to be a maximum, differentiate the derivative and see if d²A/dx² at point (x = 2/3) is +/-, if plus then minimum, if - then maximum.
    It should be a negative number as you say its a maximum.

    :rolleyes: Hope that helps, if you need further help, just ask.

    Vijay
 
 
 
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