The total cost to produce x boxes of cookies is C dollars, where C = 0.0001x3...

 

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The total cost to produce x boxes of cookies is C dollars, where C = 0.0001x3 - 0.04x2 + 2x + 400. In t weeks, production is estimated to be x = 1400 + 100t boxes. (a) Find the marginal cost C'(x). C'(x) = (b) Use Leibniz's notation for the chain rule, dC dt = dC = dC . dt dx dx to find the rate with respect to time t that the cost is changing. dt (c) Use the results from part (b) to determine how fast costs are increasing (in dollars per week) when t = 4 weeks. dollars per week The total cost to produce x boxes of cookies is C dollars, where C = 0.0001x3 - 0.04x2 + 2x + 400. In t weeks, production is estimated to be x = 1400 + 100t boxes. (a) Find the marginal cost C'(x). C'(x) = (b) Use Leibniz's notation for the chain rule, dC dt = dC = dC . dt dx dx to find the rate with respect to time t that the cost is changing. dt (c) Use the results from part (b) to determine how fast costs are increasing (in dollars per week) when t = 4 weeks. dollars per week