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Finding rate of change

Ex 6.1, 15 - The total cost C(x) = 0.007 x3 - 0.003 x2 - Ex 6.1

Ex 6.1,15 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1,15 - Chapter 6 Class 12 Application of Derivatives - Part 3


Transcript

Ex 6.1, 15 The total cost C(π‘₯) in Rupees associated with the production of π‘₯ units of an item is given by 𝐢(π‘₯) = 0.007π‘₯^3 – 0.003π‘₯2 + 15π‘₯ + 4000. Find the marginal cost when 17 units are produced.Since Marginal Cost is Rate of change in Total Cost w.r.t No of units produced Let MC be marginal cost So, MC = 𝒅π‘ͺ/𝒅𝒙 Given, Total Cost = C(π‘₯) =0.007π‘₯^3βˆ’0.003π‘₯^2+15π‘₯+4000" " We need to find marginal Cost when 17 units are produced i.e. MC when π‘₯ = 17 MC = 𝑑(𝐢(π‘₯))/𝑑π‘₯ MC = 𝑑(0.007π‘₯^3 βˆ’ 0.003π‘₯^2 + 15π‘₯ + 4000)/𝑑π‘₯ MC = 𝑑(0.007π‘₯^3 )/𝑑π‘₯ βˆ’ 𝑑(0.003π‘₯^2 )/𝑑π‘₯+ 𝑑(15π‘₯)/𝑑π‘₯+ 𝑑(4000)/𝑑π‘₯ MC = 0.007 𝑑(π‘₯^3 )/𝑑π‘₯ βˆ’0.003 𝑑(π‘₯^2 )/𝑑π‘₯ + 15𝑑(π‘₯)/𝑑π‘₯+0 MC = 0.007 Γ— 3π‘₯^2βˆ’0.003 Γ—2π‘₯+15 MC = 0.021π‘₯^2βˆ’0.006π‘₯+15 We need to find MC when π‘₯=17 Putting 𝒙=πŸπŸ• MC = 0.021(17)^2βˆ’0.006(17)+15 MC = 6.069 – 0.102 + 15 MC = 20.967 Hence, the Required Marginal cost is Rs. 20.967

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.