Marginal cost & cost function

 The cost to produce an additional item is called the marginal cost and as we've illustrated in the above example the marginal cost is approximated through the rate of change of the cost function, C ( x ) .  Therefore, we described the marginal cost function to be the derivative of the cost function or, C′ ( x ) .  Let's work a rapid example of this.

Example   The production costs per day for some widget is specified by,

                        C ( x ) = 2500 -10x - 0.01x² + 0.0002x³

What is the marginal cost while x = 200 , x = 300 & x = 400 ?

Solution

Therefore, we require the derivative and then we'll require computing some values of the derivative.

C′ ( x ) = -10 - 0.02 x + 0.0006 x²

C′ ( 200) = 10       C′ (300) =38                       C′ ( 400) = 78

Thus, in order to generates the 201st widget it will cost approximately $10. To generate the 301^st widget will cost around $38.  At last, to product the 401^st widget it will cost approximately $78.