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 f'(x) is the total production cost. Its units are dollars. 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 average 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. (b) What does the statement f'(600) = 14 mean? O After 600 ounces of gold have been produced, the average production cost is $14/ounce. So the cost of producing 600 ounces is about $14/ounce. O The total cost to produce 14 ounces of gold is approximately $600. O After 600 ounces of gold have been produced, the rate at which the production cost is increasing is $14/ounce. So the cost of producing the 600th (or 601st) ounce is about $14. O After 14 ounces of gold have been produced, the average production cost is $600/ounce. So the cost of producing 14 ounces is about $600/ounce. (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) wil---Select--- because more efficient use is made of start-up costs as x increases. But eventually f'(x) might ---Select--- due to large-scale operations ---Select-- increase decrease
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 f'(x) is the total production cost. Its units are dollars. 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 average 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. (b) What does the statement f'(600) = 14 mean? O After 600 ounces of gold have been produced, the average production cost is $14/ounce. So the cost of producing 600 ounces is about $14/ounce. O The total cost to produce 14 ounces of gold is approximately $600. O After 600 ounces of gold have been produced, the rate at which the production cost is increasing is $14/ounce. So the cost of producing the 600th (or 601st) ounce is about $14. O After 14 ounces of gold have been produced, the average production cost is $600/ounce. So the cost of producing 14 ounces is about $600/ounce. (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) wil---Select--- because more efficient use is made of start-up costs as x increases. But eventually f'(x) might ---Select--- due to large-scale operations ---Select-- increase decrease
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 f'(x) is the total production cost. Its units are dollars.
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 average 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.
(b) What does the statement f'(600) = 14 mean?
O After 600 ounces of gold have been produced, the average production cost is $14/ounce. So the cost of producing 600 ounces is about $14/ounce.
O The total cost to produce 14 ounces of gold is approximately $600.
O After 600 ounces of gold have been produced, the rate at which the production cost is increasing is $14/ounce. So the cost of producing the 600th (or 601st)
ounce is about $14.
O After 14 ounces of gold have been produced, the average production cost is $600/ounce. So the cost of producing 14 ounces is about $600/ounce.
(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) wil---Select---because more efficient use is made of start-up costs as x increases. But eventually f'(x) might
---Select--- due to large-scale operations
-Select---
increase
decrease
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