Show all work, thanks. ### Minimizing Average Costs for Super Bowl CommercialsThe 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.

Note:- These are multiple sub parts question and according to Bartleby guideline we can do maximum 3…

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

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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Show all work, thanks.

### 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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