The cost C (in dollars) of manufacturing x number of high-quality computer laser printers is C(x)=15x^(4/3)+15x^(2/3)+600,000.

Question

The cost C (in dollars) of manufacturing x number of high-quality computer laser printers is C(x)=15x^(4/3)+15x^(2/3)+600,000.

Currently, the level of production is 1,728 printers, but that level is increasing by 50 every month. At what rate is the cost increasing every month?

Answer 1

C'(x) = (20x^1/3 + 10x^-1/3)·x'; C'(1728) = (20·1728^1/3 + 10·1728^-1/3)·50 = $12041.67 per month