The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 – 0.02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.
C(x) = 0.005
– 0.02
+ 30x + 5000
Marginal Cost(
) = 
(C(x))
= (0.005
3
– (0.02
2x) + 30
∵ x = 3
= (0.005
3
9) – (0.02
2
3) + 30
= 30.135 – 0.12
= 30.015
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