Answer:
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.