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The cost (in dollars) of producing x units of a certain commodity is C(x) = 6000 + 5x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) X = 104 $ per unit (ii) X = 101 $ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit

The cost (in dollars) of producing x units of a certain commodity is C(x) = 6000 + 5x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) X = 104 $ per unit (ii) X = 101 $ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The cost (in dollars) of producing x units of a certain commodity is C(x) = 6000 + 5x + 0.15x2. %3D (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) X = 104 $ per unit (ii) X = 101 $ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit
Transcribed Image Text:The cost (in dollars) of producing x units of a certain commodity is C(x) = 6000 + 5x + 0.15x2. %3D (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) X = 104 $ per unit (ii) X = 101 $ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit
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 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. 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. (b) What does the statement f'(700) = 11 mean? %D After 700 ounces of gold have been produced, the average production cost is $11/ounce. So the cost of producing 700 ounces is about $11/ounce. The total cost to produce 11 ounces of gold is approximately $700. After 700 ounces of gold have been produced, the rate at which the production cost is increasing is $11/ounce. So the cost of producing the 700th (or 701st) ounce is about $11. After 11 ounces of gold have been produced, the average production cost is $700/ounce. So the cost of producing 11 ounces is about $700/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) will - --Select--- 0 because more efficient use is made of start-up costs as x increases. But eventually f'(x) might ---Select--- e due to large-scale operations.
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? 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. 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. (b) What does the statement f'(700) = 11 mean? %D After 700 ounces of gold have been produced, the average production cost is $11/ounce. So the cost of producing 700 ounces is about $11/ounce. The total cost to produce 11 ounces of gold is approximately $700. After 700 ounces of gold have been produced, the rate at which the production cost is increasing is $11/ounce. So the cost of producing the 700th (or 701st) ounce is about $11. After 11 ounces of gold have been produced, the average production cost is $700/ounce. So the cost of producing 11 ounces is about $700/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) will - --Select--- 0 because more efficient use is made of start-up costs as x increases. But eventually f'(x) might ---Select--- e due to large-scale operations.
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