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    I am doing some maths coursework for my Access Business Studies course and I am stuck on a question.

    Here it is:

    Your firm is considering launching a new product. A marketing comparision with other similar products has led your marketing departament to believe that the amount of the product sold will vary over time according to the following equation.

    q= -1/3t³ - t² +168t

    where q is the number of units sold at time t(months)

    use differential calculus:
    (i) find the point in time when maximum sales can be expected;
    (ii) show that this is a maximum

    Any help would be greatly appreciated

    Thanks
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    To find a maximum (or turning points, for that matter) you need to differentiate the function, and equate to 0.

    dq/dt = -t2 - 2t + 168 = 0

    t2+2t-168 = 0

    (t-12)(t+14) = 0

    t = 12 months (t cannot be -14, since it can't be <0 )

    Differentiate again, to find out more about the nature of the turning points:

    d2q/dt2 = -2t - 2

    Sub t=12: d2q/dt2 = -24 - 2 = -26
    Since d2q/dt2 < 0 at t=12, this is a maximum turning point on the curve, and hence a maximum for sales.
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    Thanks so much for your help.
    If its not too much trouble could you have a look at another question.
    I have been working on this coursework all day because I have to hand it in tomorrow and my brain has gone dead.


    A supermarket is considering introducing a new savings scheme amongst their work force. If above 90% say yes that they will implement the scheme A sample of 300 was taken and 240 said yes they would use the scheme. Using 95% confidence interval test whether the scheme should be adopted.
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    Sorry, I just don't know what a confidence interval test is. I'm guessing it's like doing a hypothesis test.
    But I just don't know...
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    I always did confidence interval tests by normalising the data so that the mean = 0 and variance = 1 and then looking it up on the normal distribution tables. Don't have a clue about it in this context I'm afraid.
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    ok thanks guys
 
 
 
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