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, '(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 C(x) at value 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.
Please mark your answers with an appropriate letter (A-E) and put answers in alphabetical order. Then scan your work to a PDF file and upload it for your answer to this question.