Finding rate of change

Chapter 6 Class 12 Application of Derivatives (Term 1)
Concept wise

### 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 πΆ(π₯) = 0.007π₯^3 β 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 = ππͺ/ππ Given, Total Cost = C(π₯) =0.007π₯^3β0.003π₯^2+15π₯+4000" " We need to find marginal Cost when 17 units are produced i.e. MC when π₯ = 17 MC = π(πΆ(π₯))/ππ₯ MC = π(0.007π₯^3 β 0.003π₯^2 + 15π₯ + 4000)/ππ₯ MC = π(0.007π₯^3 )/ππ₯ β π(0.003π₯^2 )/ππ₯+ π(15π₯)/ππ₯+ π(4000)/ππ₯ MC = 0.007 π(π₯^3 )/ππ₯ β0.003 π(π₯^2 )/ππ₯ + 15π(π₯)/ππ₯+0 MC = 0.007 Γ 3π₯^2β0.003 Γ2π₯+15 MC = 0.021π₯^2β0.006π₯+15 We need to find MC when π₯=17 Putting π=ππ MC = 0.021(17)^2β0.006(17)+15 MC = 6.069 β 0.102 + 15 MC = 20.967 Hence, the Required Marginal cost is Rs. 20.967