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MarginalsandDifferentials 2.6 OBJECTIVE • Find marginal cost, revenue, and profit. • Find ∆y and dy. • Use differentials for approximations. 2012 Pearson Education, Inc. All rights reserved Slide 2.6-2 2.6MarginalsandDifferentials DEFINITIONS: Let C(x), R(x), and P(x) represent, respectively, the total cost, revenue, and profit from the production and sale of x items. The marginal cost at x, given by C¢ (x), is the approximate cost of the (x + 1)th item: C¢ (x) ≈ C(x + 1) – C(x), or C(x + 1) ≈ C(x) + C¢ (x). 2012 Pearson Education, Inc. All rights reserved Slide 2.6-3 2.6MarginalsandDifferentials DEFINITIONS (concluded): The marginal revenue at x, given by R¢ (x), is the approximate revenue from the (x + 1)th item: R¢ (x) ≈ R(x + 1) – R(x), or R(x + 1) ≈ R(x) + R¢ (x). The marginal profit at x, given by P¢ (x), is the approximate profit from the (x + 1)th item: P¢ (x) ≈ P(x + 1) – P(x), or P(x + 1) ≈ P(x) + P¢ (x). 2012 Pearson Education, Inc. All rights reserved Slide 2.6-4 2.6MarginalsandDifferentials Example 1: Given C(x) = 62x2 + 27,500 and R(x) = x3 12x2 + 40x +10 find each of the following: a) Total profit, P(x). b) Total cost, revenue, and profit from the production and sale of 50 units of the product. c) The marginal cost, revenue, and profit when 50 units are produced and sold. 2012 Pearson Education, Inc. All rights reserved Slide 2.6-5 ... - tailieumienphi.vn
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