For the cost function, find the marginal cost at the given production level x. Round your answer to two decimal places.
$C ( x ) = 30,000 + 10 x - \frac { x ^ { 2 } } { 10,000 } , x = 2,000$
A)$9.60 per item
B) $9.58 per item
C) $10.00 per item
D) $9.61 per item
E) $10.40 per item

Question

For the cost function, find the marginal cost at the given production level x. Round your answer to two decimal places. 
  $C ( x ) = 30,000 + 10 x - \frac { x ^ { 2 } } { 10,000 } , x = 2,000$  
A)$9.60 per item
B) $9.58 per item
C) $10.00 per item
D) $9.61 per item
E) $10.40 per item

Quizplus · Accepted Answer

The marginal cost is the derivative of the cost function with respect to x. The derivative of $C(x) = 30,000 + 10x - \frac{x^2}{10,000}$ is $C'(x) = 10 - \frac{x}{5,000}$. Evaluating this at $x = 2,000$, we get $C'(2,000) = 10 - \frac{2,000}{5,000} = 10 - 0.4 = 9.6$. Thus, the marginal cost is $9.60 per item.

For the Cost Function, Find the Marginal Cost at the Given