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    In 8i, I keep getting x=8 instead of x=4 like in the mark scheme. Can someone please show the working? (probably my algebra is wrong)
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    When I do part ii, I also keep getting x=8 instead of x= 8 or 0.
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    What did you get when you differentiated?


    :When you differentiate the bit in the brackets you get (8 - 2x) and so for dy/dx to be zero, (8 - 2x)  must be zero which definitely means x=4.:
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    I got -x(8x-x^2)^-0.5.
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    I don't agree.

    How are you doing it, can you show me your working? It looks as though you are not differentiating correctly.

    Meanwhile I'll do the working to show you.
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    I see that it’s x(8x-x^2)^-0.5. But when I make it equal to 0 to find the stationary point, I don’t know how to find x.
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    I think you've only done half the differentiation (and not done it right)

    To me this is 'function of a function' and I'd do it like this (think sometimes called 'chain rule')

    Not sure what notation you use but I would do this

    y = (8x - x²) ^1/2

    So y = f ^1/2 where f = (8x - x²)

    dy/df = 1/2 f ^(-1/2) and df/dx = 8- 2x That bit in bold just because I think it's the key to the solution here

    dy/dx = dy/df . df/dx = 0.5 (8x - x²) ^(-1/2) . (8 - 2x)

    = 1/2 (8 - 2x) / (8x - x²)^1/2

    To make this = zero we need the top bit to equal zero therefore 8 - 2x = 0 and solve for x
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    Thank you, but how did you make it into division in the last line of your working?
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    Differentiating the (.... ) ^1/2 bit makes it 1/2 ( ....) ^-1/2

    So that -1/2 power means I can put it on the bottom and make the power + instead
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    Thank you so much phys981! You have probably raised me a grade already.
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