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11 September, 03:38

The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f (p). (a) What is the meaning of the derivative f ' (5) ? The rate of change of the price per pound with respect to the quantity of coffee sold. The supply of coffee needed to be sold to charge $5 per pound. The rate of change of the quantity of coffee sold with respect to the price per pound when the price is $5 per pound. The rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound. The price of the coffee as a function of the supply. What are the units of f ' (5) ? dollars dollars/pound pounds / (dollars/pound) pounds dollars / (pound/pound) pounds/dollar

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  1. 11 September, 06:26
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    a. The rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound.

    b. pounds/dollar

    Explanation:

    (a) What is the meaning of the derivative f ' (5) ?

    Given Q = f (p) ... (1)

    Differentiating Q with respect to p gives us:

    qQ/dp = f' (p) ... (2)

    Equation (2) implies the rate of change of the price per pound with respect to the quantity of coffee sold.

    When p = 5, we have:

    qQ/dp = f' (5) ... (3)

    Equation (3) implies the rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound.

    (b) What are the units of f' (5) ?

    Since we have qQ/dp = f' (5) as shown in equation (3), it implies that the units of of f' (5) are pounds/dollar.
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