Question

the cost function for production of a commodity is c(x)=339+25x-0.09x^2+0.0004x^3. a.find and interpret c'(100) b. compare c'(100) with the cost of producing 101st item.

Answer 1

c(x) = 0.0004x³ -0.09x² +25x + 339
c'(x) = 0. 0012x² - 0.18x + 25
c' (100) = 12 - 18 + 25 = 19
Marginal cost at 100 units is $19 per unit.
C(101) = 0.0004 ( 101)³ - 0.09 ( 101)² + 25 * 101 + 339

Cost of 101st item: C(101) - C ( 100)

Answer 2

Plug the value x =100 and x =101, subtract!

Answer 3

=> the difference between real unit price and marginal unit price!