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Consider the following question and a student's proposed solution. Determine if the student is correct. If not correct, identify the mistake(s) and answer the question correctly. Question. A gas station company finds that with annual upkeep and certification, the maintenance cost (in hundreds of dollars) after æ years for each fuel pump is C (x) = 8 – 1.2x + 0.022². After how many years is the average cost of the fuel pumps minimized? Student's work: Step 1: Find the derivative of C (x). C' (x) = -1.2 + 0.04x = (0.04) (x – 30). Step 2: Find the average cost of the derivative of C (x). Chue: (0.04)(x-30) Step 3: Use a derivative test and determine that at x = 30 is a relative minimum. Step 4: Make conclusion. The average cost is minimized after 30 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. The correct answer is: The average cost is minimized after g = 20 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. Since the student found the average cost anyway, there is no change in the answer. The correct answer is still: The average cost is minimized after g = 30 years. O The student made an error in finding the derivative. The correct answer is: The average cost cannot be minimized as the expenditures will continually increase. The student made no errors. His answer is correct.

Consider the following question and a student's proposed solution. Determine if the student is correct. If not correct, identify the mistake(s) and answer the question correctly. Question. A gas station company finds that with annual upkeep and certification, the maintenance cost (in hundreds of dollars) after æ years for each fuel pump is C (x) = 8 – 1.2x + 0.022². After how many years is the average cost of the fuel pumps minimized? Student's work: Step 1: Find the derivative of C (x). C' (x) = -1.2 + 0.04x = (0.04) (x – 30). Step 2: Find the average cost of the derivative of C (x). Chue: (0.04)(x-30) Step 3: Use a derivative test and determine that at x = 30 is a relative minimum. Step 4: Make conclusion. The average cost is minimized after 30 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. The correct answer is: The average cost is minimized after g = 20 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. Since the student found the average cost anyway, there is no change in the answer. The correct answer is still: The average cost is minimized after g = 30 years. O The student made an error in finding the derivative. The correct answer is: The average cost cannot be minimized as the expenditures will continually increase. The student made no errors. His answer is correct.

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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Consider the following question and a student's proposed solution. Determine if the student is correct. If not correct, identify the mistake(s) and answer the question correctly. Question. A gas station company finds that with annual upkeep and certification, the maintenance cost (in hundreds of dollars) after æ years for each fuel pump is C (x) = 8 – 1.2x + 0.022². After how many years is the average cost of the fuel pumps minimized? Student's work: Step 1: Find the derivative of C (x). C' (x) = -1.2 + 0.04x = (0.04) (x – 30). Step 2: Find the average cost of the derivative of C (x). Chue: (0.04)(x-30) Step 3: Use a derivative test and determine that at x = 30 is a relative minimum. Step 4: Make conclusion. The average cost is minimized after 30 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. The correct answer is: The average cost is minimized after g = 20 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. Since the student found the average cost anyway, there is no change in the answer. The correct answer is still: The average cost is minimized after g = 30 years. O The student made an error in finding the derivative. The correct answer is: The average cost cannot be minimized as the expenditures will continually increase. The student made no errors. His answer is correct.
Transcribed Image Text:Consider the following question and a student's proposed solution. Determine if the student is correct. If not correct, identify the mistake(s) and answer the question correctly. Question. A gas station company finds that with annual upkeep and certification, the maintenance cost (in hundreds of dollars) after æ years for each fuel pump is C (x) = 8 – 1.2x + 0.022². After how many years is the average cost of the fuel pumps minimized? Student's work: Step 1: Find the derivative of C (x). C' (x) = -1.2 + 0.04x = (0.04) (x – 30). Step 2: Find the average cost of the derivative of C (x). Chue: (0.04)(x-30) Step 3: Use a derivative test and determine that at x = 30 is a relative minimum. Step 4: Make conclusion. The average cost is minimized after 30 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. The correct answer is: The average cost is minimized after g = 20 years. The student made an error by finding the derivative of the cost function instead of finding the average cost function first and then taking the derivative. Since the student found the average cost anyway, there is no change in the answer. The correct answer is still: The average cost is minimized after g = 30 years. O The student made an error in finding the derivative. The correct answer is: The average cost cannot be minimized as the expenditures will continually increase. The student made no errors. His answer is correct.
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