The total cost C (x) in Rupees associated with the production of x units of an item is given by C (x) = 0.007x³ - 0.003x² + 15x + 4000. Find the marginal cost when 17 units are produced

Solution:

Derivatives are used to find the rate of changes of a quantity with respect to the other quantity. By using the application of derivatives we can find the approximate change in one quantity with respect to the change in the other quantity.

They are used in many situations like finding maxima or minima of a function, finding the slope of the curve, and even inflection points

Marginal cost (MC) is the rate of change of the total cost with respect to the output.

Therefore,

MC = dC/dx

= 0.007 3x² - 0.003(2x) + 15

= 0.021x² - 0.006x + 15

When x = 17

Then,

MC = 0.021(17)² - 0.006 (17) + 15

= 0.021(289) - 0.006 (17) + 15

= 6.069 - 0.102 + 15

= 20.967

So, when 17 units are produced, the marginal cost is ₹ 20.967

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.1 Question 15