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

question 45

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The marginal cost function C(x) C ^ { \prime } ( x ) is defined to be the derivative of the cost function. If the marginal cost of manufacturing xx units of a product is
C(x) =0.009x21.8x+9C ^ { \prime } ( x ) = 0.009 x ^ { 2 } - 1.8 x + 9 (measured in dollars per unit) and the fixed start-up cost is C(0) =2,200,000C ( 0 ) = 2,200,000 , use the Total Change Theorem to find the cost of producing the first 5,000 units.

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