2. [-I1 Points] DETAILS WANEAC7 4.2.005. MY NOTES PRACTICE ANOTHER Find the marginal cost, marginal revenue, and marginal prot functions. C(x) = 4x; R(x) = 9x 0.001x2 marginal cost marginal revenue marginal prot Find all values of x for which the marginal prot is zero. (Enter your answers as a comma-separated list.) x: Need Help? Submit Answer ' Submit Answer ' 3. [-I8 Points] DETAILS WANEAC7 4.2.009. MY NOTES PRACTICE ANOTHER The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 2,000x + 0.07x2. (a) Find the marginal cost function C'(x). HINT [See Example 1.] C'(x) = Use it to estimate how fast the cost is increasing when x = 4. thousand dollars per television commercial Compare this with the exact cost of airing the fth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fth commercial is $ . Thus, there is a difference of $ (b) Find the average cost function (2, and evaluate 5(4). HINT [See Example 2.] E(x) = 5(4) = thousand dollars per television commercial What does the answer tell you? The average cost of airing the rst four commercials is $ per commercial. Need Help? 4. [-l1 Points] DETAILS WAN EAC7 4.2.014. MY NOTES PRACTICE ANOTHER The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising "Eatathon." The society will charge students $1.10 per sewing of pasta. The society estimates that the total cost of producing X servings of pasta at the event will be C(x) = 370 + 0.10x + 0.002X2 dollars. (a) Calculate the marginal revenue R'(x) and prot P'(x) functions. R'(X) = P'(X) (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 200 servings of pasta (in $). revenue prot marginal revenue per additional plate {Ii-W436} marginal prot per additional plate Interpret the results. The approximate ~-Select--- a from the sale of the 2015': plate of pasta is $ (c) For which value of x is the marginal prot zero? x = plates Interpret your answer. The graph of the profit function is a parabola with a vertex at x = , so the loss is at a minimum when you produce and sell plates. Need Help? 3. [-/1 Points] DETAILS WANEAC7 4.3.021. MY NOTES PRACTICE ANOTHER Calculate dy Simplify your answer. HINT [See Examples 1 and 2.] dx 5x + 8 y = 7x - 1 dy dx Need Help? Read It 4. [-/1 Points] DETAILS WANEAC7 4.3.030. MY NOTES PRACTICE ANOTHER Calculate . You need not expand your answer. dx y = (8x + x) (x - x2) dy dx Need Help? Read It5. [-/1 Points] DETAILS WANEAC7 4.3.044. MY NOTES PRACTICE ANOTHER Calculate ay You need not expand your answer. dx y = 7x2 - 9x + 13 2x + 4 dy dx Need Help? Read It1. [-/1 Points] DETAILS WANEAC7 4.4.003. MY NOTES PRACTICE ANOTHER Calculate the derivative of the function. HINT [See Example 1.] f( x) = (x - 1)-1 f' ( x ) = Need Help? Read It 2. [-/1 Points] DETAILS WANEAC7 4.4.009. MY NOTES PRACTICE ANOTHER Calculate the derivative of the function. HINT [See Example 1.] f ( x ) = 1 3X - f'( x ) = Need Help? Read It Submit Answer3. [-/1 Points] DETAILS WANEAC7 4.4.004. MY NOTES PRACTICE ANOTHER Calculate the derivative of the function. HINT [See Example 1.] f(x) = (2x - 1) -2 f' ( x ) = Need Help? Read It 4. [-/1 Points] DETAILS WANEAC7 4.4.012.MI. MY NOTES PRACTICE ANOTHER Calculate the derivative of the function. HINT [See Example 1.] f(x) = (x10 - x) 10 Need Help? Read It Master It5. [-11 Points] DETAILS WANEAC7 4.4.016. MY NOTES | PRACTICE ANOTHER Calculate the derivative of the function. g(X) = (2x2 + x + 1)3 9'(X) = Need Help? 6. [-11 Points] DETAILS WANEAC7 4.4.024. MY NOTES | PRACTICE ANOTHER Calculate the derivative of the function. f(X)=\\/5x+x2 f'(x) = Need Help? 7. [-/1 Points] DETAILS WANEAC7 4.4.037.MI. MY NOTES PRACTICE ANOTHER Calculate the derivative of the function. s ( x ) = 2x + 8 3x - S'( X ) = Need Help? Read It Master It 8. [-/1 Points] DETAILS WANEAC7 4.4.002. MY NOTES PRACTICE ANOTHER Calculate the derivative of the function. f (x) = (7x - 1)2 f' ( x ) = Need Help? Read It