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    I'm stuck on the second part, the first part was easy, however i've had trouble manipulating the second derivative to show prove part 2 of the question.

    The question,first part and second derivative is in the images.







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    If it's a maximum point then just show that given the conditions in the question that  f''(x) < 0 .
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    (Original post by B_9710)
    If it's a maximum point then just show that given the conditions in the question that  f(x) < 0 .
    What tools would I need to differentiate that function?

    it looks very hard but very easy at teh same time
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    (Original post by Duck'sBack)
    What tools would I need to differentiate that function?

    it looks very hard but very easy at teh same time
    (I've edited my post).
    You have differentiated it, assuming it is correct, all you have to do is show that if n is even and m is odd that  f''(x) must be even. You have to remember that you have already shown 0<x<1. Use these few points and try and show that f''(x)<0
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    (Original post by B_9710)
    (I've edited my post).
    You have differentiated it, assuming it is correct, all you have to do is show that if n is even and m is odd that  f''(x) must be even. You have to remember that you have already shown 0<x<1. Use these few points and try and show that f''(x)<0
    You really need to get into the habit of looking at peoples usernames
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    (Original post by Duck'sBack)
    You really need to get into the habit of looking at peoples usernames
    Perhaps you're right.
    Product rule is all you need here.
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    (Original post by Duck'sBack)
    What tools would I need to differentiate that function?

    it looks very hard but very easy at teh same time
    You'd need to use the product rule, and I guess technically the chain rule on the (x-1)^n term - that or I guess you could use the binomial formula to write this out as a sum, and differentiate term by term, but that's more effort than it's worth.
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    (Original post by hamzah0608)
    I'm stuck on the second part, the first part was easy, however i've had trouble manipulating the second derivative to show prove part 2 of the question.

    The question,first part and second derivative is in the images.
    Life would have been a hell of a lot simpler if you'd written f'(x) in terms of f(x)... just sayin'.
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    (Original post by B_9710)
    Perhaps you're right.
    Product rule is all you need here.
    This is like a C2 question don't you think
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    (Original post by Duck'sBack)
    This is like a C2 question don't you think
    :hand:
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    (Original post by B_9710)
    :hand:
    What does that mean? You trying to be racist?
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    (Original post by Duck'sBack)
    What does that mean? You trying to be racist?
    You saw right through me.
 
 
 
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