# Example 5

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 5 The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x3 – 0.02 x2 + 30x + 5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output. Marginal cost is the rate of change of total cost w.r.t output (unit produce) Let MC be marginal cost ∴ MC = 𝑑𝐶𝑑𝑥 It is given C(𝑥) = 0.005𝑥3 – 0.02𝑥2 + 30𝑥 + 5000 We need to find marginal cost when 3 unit produced i.e. need to find MC = 𝑑𝐶𝑑𝑥 at 𝑥 = 3 Now, MC = 𝑑(𝑐)𝑑𝑥 MC = 𝑑0.05𝑥3 − 0.02𝑥2 + 30 + 5000𝑑𝑥 MC = 𝑑0.05𝑥3𝑑𝑥 – 𝑑(0.02𝑥2)𝑑𝑥 + 𝑑 (30𝑥)𝑑𝑥 + 𝑑 5000𝑑𝑥 MC = 3 × 0.05x2 – 2 × 0.02x + 30 + 0 MC = 0.015x2 – 0.04x + 30 We need MC at 𝑥 = 3 Putting 𝑥= 3 MC = 0.015(32) – 0.04 (3) + 30 MC = 30.015 Hence, Required marginal cost is Rs. 30.02 (nearly)

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Chapter 6 Class 12 Application of Derivatives

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.