The total profit in thousands of dollars, for a product is given by (see attachment) and x is the number of units produced. Determine the marginal profit function when x=15.

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The total revenue for a product can be calculated as the area under the demand curve. Suppose that the demand curve for a certain wine (in dollars per liter) is given by the following, where is the demand in liters. Estimate the total revenue using rectangles of width 10 ters D(4) = ² -10q+267 for 0 sqs50 The approximate revenue using left endpoints is The approximate revenue using right endpoints is $ The approximate revenue using the average is $

Assume that it costs a company approximately C(x) = 400,000 + 120x + 0.002x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.