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.

Cost of 101st item: C(101) - C ( 100) 
Plug the value x =100 and x =101, subtract!

C(101) = 0.0004 ( 101)³ - 0.09 ( 101)² + 25 * 101 + 339 = 2358,0304
C(100) = 0.0004 ( 100)³ - 0.09 ( 100)² + 25 * 100 + 339 = 2339

C(101) - C ( 100) = 2358,0304 - 2339 = 19,0304