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Math Help - Differentiation: optimisation help.

  1. #1
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    Differentiation: optimisation help.

    So I have been under a lot of stress lately and have been trying to complete things for my other units. Because of this I have neglected maths for the last two weeks (I am catching up this weekend) and I am unable to complete these online quiz questions. I am probably breaking some kind of forum rule by asking you guys for direct answers, but I would really appreciate it (as I have tried for ages and I just have no idea how to do them)

    1.

    The total profit $P, generated from the production and marketing of n items of a certain product is given by
    P = −46800 n−6 n3+1350 n2−116
    How many items should be made for maximum profit? What is the maximum profit?

    Enter your answers as a list [in square brackets] of the form: [ n, p]
    for some number of items n and profit p (in dollars, but don't include the dollar sign).

    2. Find the value of x that minimises
    y = 10 x2 + 2700

    x
    for positive x.



    a.

    In order to do that first find the derivative dy/dx.
    dy/dx =

    b.

    How many critical numbers does y have, for positive x?
    Recall that a critical number of a function is a value of x for which the derivative of the function is zero or doesn't exist.

    c.

    What is the nature of the critical number of the previous part?
    Enter m for minimum, M for maximum or i for a horizontal point of inflection.

    3.

    A piece of cardboard measures 5 cm by 8 cm. Two equal squares are removed from a 5 cm side as shown below. Two equal rectangles are removed from the other corners so that the remaining material can be folded to form a rectangular box with a lid.

    (image that goes with it) http://desmond.imageshack.us/Himg826...if&res=landing

    4.

    You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 30 cm3, what values of h and r will minimise the total surface area (including the top and bottom faces)? Give your answers correct to 2 decimal places as a list [in brackets] of the form: [ h, r ]
    for constants h (height), r (radius), in that order.

    I would really appreciate any help given. Thankyou.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Re: Differentiation: optimisation help.

    I am probably breaking some kind of forum rule by asking you guys for direct answers ...
    ... and that would be true. Show some attempt at trying to work these problems on your own and someone may provide guidance.
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