The cost of producing x ounces of gold from a new gold mine is C = f(x) dollars. (a) What is the meaning of the derivative f ′(x)? What are its units? f ′(x) is the total amount of gold produced. Its units are ounces. f ′(x) is the rate of change of the production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. f ′(x) is the average production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. f ′(x) is the total production cost. Its units are dollars. (b) What does the statement f ′(700) = 18 mean? The total cost to produce 18 ounces of gold is approximately $700. After 18 ounces of gold have been produced, the average production cost is $700/ounce. So the cost of producing 18 ounces is about $700/ounce. After 700 ounces of gold have been produced, the average production cost is $18/ounce. So the cost of producing 700 ounces is about $18/ounce. After 700 ounces of gold have been produced, the rate at which the production cost is increasing is $18/ounce. So the cost of producing the 700th (or 701st) ounce is about $18. (c) Do you think the values of f ′(x) will increase or decrease in the short term? What about the long term? Explain. In the short term, the values of f '(x) will because more efficient use is made of start-up costs as x increases. But eventually f '(x) might due to large-scale operations.