Consider the marginal cost function C′​(x)=400+8x−0.01x^2.   a. Find the additional cost incurred in dollars when production is increased from 150 units to 200 units. b. Find the additional cost incurred in dollars when production is increased from 500 units to 550 units.

The marginal profit from selling x chairs is P'(x)=-10x2 +100x+50 dollars per chair. There are no fixed costs to consider. What is the total profit realized from producing 10 chairs?

You have been placed in charge of minimizing costs on a production line. The cost model is C=100x-12^2+3x^3. The variable x represents the level of production for the given cost. Determine the production level that minimizes the average cost. A.)  Find the marginal cost.  (Divide by x and take 1st derivative) B.)  What is the production level?

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.