The Marginal Cost Function $C ^ { \prime } ( x )$

Short Answer

The marginal cost function $C ^ { \prime } ( x )$ is defined to be the derivative of the cost function. If the marginal cost of manufacturing $x$ units of a product is
$$C ^ { \prime } ( x ) = 0.009 x ^ { 2 } - 1.8 x + 9$$
(measured in dollars per unit) and the fixed start-up cost is $C ( 0 ) = 1,800,000$ , use the Total Change Theorem to find the cost of producing the first 5,000 units.