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

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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