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? O r(x) is the average production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. O r(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. O r(x) is the total amount of gold produced. Its units are ounces. O r(x) is the total production cost. Its units are dollars. (b) What does the statement f(400) = 11 mean? O After 400 ounces of gold have been produced, the rate at which the production cost is increasing is $11/ounce. So the cost of producing the 400th (or 401st) ounce is about $11. After 11 ounces of gold have been produced, the average production cost is $400/ounce. So the cost of producing 11 ounces is about $400/ounce. After 400 ounces of gold have been produced, the average production cost is $11/ounce. So the cost of producing 400 ounces is about $11/ounce. The total cost to produce 11 ounces of gold is approximately $400. (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 -Select-- x increases. But eventually f'(x) might -Select- because more efficient use is made of start-up costs as due to large-scale operations.
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? O r(x) is the average production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. O r(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. O r(x) is the total amount of gold produced. Its units are ounces. O r(x) is the total production cost. Its units are dollars. (b) What does the statement f(400) = 11 mean? O After 400 ounces of gold have been produced, the rate at which the production cost is increasing is $11/ounce. So the cost of producing the 400th (or 401st) ounce is about $11. After 11 ounces of gold have been produced, the average production cost is $400/ounce. So the cost of producing 11 ounces is about $400/ounce. After 400 ounces of gold have been produced, the average production cost is $11/ounce. So the cost of producing 400 ounces is about $11/ounce. The total cost to produce 11 ounces of gold is approximately $400. (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 -Select-- x increases. But eventually f'(x) might -Select- because more efficient use is made of start-up costs as due to large-scale operations.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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?
O P(x) is the average production cost with respect to the number of ounces of gold produced. Its units are dollars per
ounce.
O 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.
O F(x) is the total amount of gold produced. Its units are ounces.
O (x) is the total production cost. Its units are dollars.
(b) What does the statement f'(400) = 11 mean?
O After 400 ounces of gold have been produced, the rate at which the production cost is increasing is $11/ounce. So
the cost of producing the 400th (or 401st) ounce is about $11.
After 11 ounces of gold have been produced, the average production cost is $400/ounce. So the cost of producing
11 ounces is about $400/ounce.
After 400 ounces of gold have been produced, the average production cost is $11/ounce. So the cost of producing
400 ounces is about $11/ounce.
The total cost to produce 11 ounces of gold is approximately $400.
(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 ---Select--
x increases. But eventually f'(x) might --Select-
because more efficient use is made of start-up costs as
|due to large-scale operations.
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