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# Help watch

1. 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
2. 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.
3. 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.
4. 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...
5. 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.
6. ok thanks guys

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