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View History Bookmarks People Window Help 99% Thu 1:08 PM Take a Test Garlyn Smith Secure https://www.mathxi.com/Student/Playermest.aspx?testld 153074412&centerwin; yes WWW Survey of Calculus, Spring 2017 Quiz: Quiz 3 Time Remaining: 00:14:42 Submit Quiz This Question: 1 pt 1 of 20 complete) This Quiz: 2 pts possible respectively, the revenue, cost, and proft, in dollars, from the production and sale ofxitems. fR(x). 4x and cux).0.003? +12x 40, find Let R(x), C(x), and P(x) be each of the following. b) R(100), C(100), and P(100) c) R'(x), C'(x), and P'(x) d) R (100), C (100), and P'(100) a) P(x) b) R(100) S P(100) ms c) R (x) d) R (100) Enter your answer in each of the answer boxes.

Explanation / Answer

a>

Profit is the total revnue minus the total cost

=> P(x) = R(x) - C(x) = 4x - (.003x^2 + 1.2x + 40) = - .003x^2 + 2.8x - 40

P(x) = - .003x^2 + 2.8x - 40

b> R(x=100) = 4x = 4*100 = 400

C(x=100) = .003x^2 + 1.2x + 40 = .003(100)^2 + 1.2(100) + 40 = 190

=> P(x=100) = R(x=100) - C(x=100) = 400 - 190 = 210

c> R'(x) = 4    {derivative of R(x)}

C'(x) = .006x + 1.2   {derivative of C(x)}

P'(x) = - .006x + 2.8

d> R'(x=100) = 4

C'(x=100) = .006(100) + 1.2 = 1.8

P'(x=100) = - .006(100) + 2.8 = 2.2

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