This may sound a bit confusing.

If there's a problem, that says: "A manufacturer finds that the daily profit, $P, from selling n articles is given by P= 100n - 0.4n^2 - 160 ", would the 'profit per article' be the derivative dP/dn, or would it be P/n? And if you want to find the value of n which maximises the profit per article, would you use the double derivative, or would you just find the maximum of the derivative of P/n?

Thanks!

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