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

question 102

Multiple Choice

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 $C ( 0 ) = 1,900,000$ , use the Total Change Theorem to find the cost of producing the first 5,000 units. Select the correct answer.

• A) \(\$ 354,645,000\)
• B) \(\$ 354,845,000\)
• C) \(\$ 354,445,000\)
• D) \(\$ 354,545,000\)
• E) \(\$ 354,745,000\)

---

Definitions:

Impending Shock

A critical condition where the body is not receiving enough blood flow, indicating that a state of shock is imminent if not promptly addressed.

Ashen

Referring to a pale, grayish skin tone, often associated with illness or shock.

Distended Veins

Veins that are enlarged, swollen, or fuller than normal, often indicating an underlying medical condition.

Capillary Filling Time

A clinical test used to assess blood circulation by applying pressure to the skin to create blanching and then observing the time it takes for color to return.