Suppose that c (x) = 3x^3-12x^2+9000x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

C (x) = 3x² (3) - 12x² (2) + 9000x

c (x) = 9x²-24x+9000

9x² (2) - 24x+9000=0

This can be factored to 3 (3x²-8x+3000)

By not producing anything we constantly escalate our cost, there is no value for x.

By using a rational expression x=4/3+i√2246/3 and x=4/3-i √2246/3