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The cost, in thousands of dollars, of airing X 30-second television C(x)=40+ 3,000x + 0.064x² Your company would like to minimize average costs, C(x), for airi A) What is C(x)? B) Compute the derivative of the function in D

The cost, in thousands of dollars, of airing X 30-second television C(x)=40+ 3,000x + 0.064x² Your company would like to minimize average costs, C(x), for airi A) What is C(x)? B) Compute the derivative of the function in D

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Do D and E. Show all work, thanks. 

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. 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.
Transcribed Image Text: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. 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.
a) What is I (x) 201² Aurage lost c(x) = ((x) x EW= 40 + 3000x + 0.0064x² 20 C (x) = 40 0.064x + 30,00 x b) Compute the derivative &'() of the function in part A. 2013 Diff E(X) W. r. to 'x' d ([(x)] = d [42] +960.064x) + d (3000) 40 dx dr Z'(x) = -40 + 0.00 64 x² 2020? 9 Where is the derivative of part & -equals Sa- put C/(x) 20 + 0.0064 20 ㅕ -0.0064 7 X2 -40 2 x² 2 -0.0064 x = √√√8250 = 9 9 20, 1 -40 x² -40 2 (0) 20 + = 6250 19.05 at X= 79.05
Transcribed Image Text:a) What is I (x) 201² Aurage lost c(x) = ((x) x EW= 40 + 3000x + 0.0064x² 20 C (x) = 40 0.064x + 30,00 x b) Compute the derivative &'() of the function in part A. 2013 Diff E(X) W. r. to 'x' d ([(x)] = d [42] +960.064x) + d (3000) 40 dx dr Z'(x) = -40 + 0.00 64 x² 2020? 9 Where is the derivative of part & -equals Sa- put C/(x) 20 + 0.0064 20 ㅕ -0.0064 7 X2 -40 2 x² 2 -0.0064 x = √√√8250 = 9 9 20, 1 -40 x² -40 2 (0) 20 + = 6250 19.05 at X= 79.05
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