Test Index

CBSE Class 12 Math 2018 Solved Paper

© examsnet.com
Question : 8 of 29
Marks: +1, -0
The total cost C(x) associated with the production of x units of an item is given by
C(x) = 0.005 x3x^3 – 0.02 x2x^2 + 30 x + 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.
Solution:  
Given C(x) = 0.005 x3x^3 – 0.02 x2x^2 + 30 x + 5000
Marginal cost is the rate of change of total cost with respect to output.
⇒ Marginal cost = dCdx\frac{dC}{dx}
⇒ Marginal cost = 0.005 (3x2)(3x^2) - 0.02 (2x) + 30 = 0.015 x2x^2 - 0.04 x + 30
Marginal cost at x 3
⇒ Marginal cost = 0.015 × 323^2 - 0.04 × 3 + 30
⇒ Marginal cost 30.015
Therefore Marginal cost is Rs. 30.015.
© examsnet.com
Go to Question:
Prev Question
Next Question