The cost, in thousands of dollars, of airing X 30-second television commercials during a Super Bowl game can be approximated by, C(x) = 40 + 3,000x + 0.064x² Your company would like to minimize average costs, C(x), for airing x commercials. Use this information to answer the questions below. A) What is C(x)? B) Compute the derivative, C'(x), of the function in Part A above. C) Where is the derivative in part B zero? SHOW WORK.
The cost, in thousands of dollars, of airing X 30-second television commercials during a Super Bowl game can be approximated by, C(x) = 40 + 3,000x + 0.064x² Your company would like to minimize average costs, C(x), for airing x commercials. Use this information to answer the questions below. A) What is C(x)? B) Compute the derivative, C'(x), of the function in Part A above. C) Where is the derivative in part B zero? SHOW WORK.
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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![### Minimizing Average Costs for Super Bowl Commercials
The cost, in thousands of dollars, of airing \( x \) 30-second television commercials during a Super Bowl game can be approximated by the function:
\[ C(x) = 40 + 3,000x + 0.064x^2 \]
Your company would like to minimize average costs, \( \overline{C}(x) \), for airing \( x \) commercials. Use this information to answer the questions below.
**A) What is \( \overline{C}(x) \)?**
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**B) Compute the derivative, \( \overline{C}'(x) \), of the function in Part A above.**
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**C) Where is the derivative in part B zero? SHOW WORK.**
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**D) Use the First or Second derivative test to prove that there is a relative minimum value of \( \overline{C}(x) \) at the value found in part C. SHOW WORK.**
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**E) How many commercials should the company air to minimize average costs? What is the minimum average cost? SHOW WORK.**
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This exercise involves understanding and calculating the average cost function derived from the given cost function, differentiating it to find the critical points, and applying derivative tests to confirm the minimum average cost.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2e37893-b1d8-4cac-bb15-a057cf9332c6%2F810cd1aa-b2f8-4ac4-9330-5ff31ee8a969%2Fyvyswrt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Minimizing Average Costs for Super Bowl Commercials
The cost, in thousands of dollars, of airing \( x \) 30-second television commercials during a Super Bowl game can be approximated by the function:
\[ C(x) = 40 + 3,000x + 0.064x^2 \]
Your company would like to minimize average costs, \( \overline{C}(x) \), for airing \( x \) commercials. Use this information to answer the questions below.
**A) What is \( \overline{C}(x) \)?**
---
**B) Compute the derivative, \( \overline{C}'(x) \), of the function in Part A above.**
---
**C) Where is the derivative in part B zero? SHOW WORK.**
---
**D) Use the First or Second derivative test to prove that there is a relative minimum value of \( \overline{C}(x) \) at the value found in part C. SHOW WORK.**
---
**E) How many commercials should the company air to minimize average costs? What is the minimum average cost? SHOW WORK.**
---
This exercise involves understanding and calculating the average cost function derived from the given cost function, differentiating it to find the critical points, and applying derivative tests to confirm the minimum average cost.
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