Question

The total cost N(x) in rupees, associated with the production of x units of an item is given by N(x)=0.06x^3-0.01x^2+10x-43. Find the marginal cost when 5 units are produced.

(a) Rs. 1.44

(b) Rs. 144.00

(c) Rs. 14.4

(d) Rs. 56.2

This question was addressed to me in an interview for internship.

Query is from Derivatives Application in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Correct answer is (b) Rs. 144.00

Easiest explanation: The marginal cost is given by the rate of change of revenue.

Hence, \(\frac{dN(x)}{dt}\)=0.18x^2-0.02x+10.

∴\(\frac{dN(x)}{dt}\)|_x=5=0.18(5)^2-0.02(5)+10

=4.5-0.1+10

=Rs. 14.4