Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by , ,where x is the number of machines used.What is the minimum average cost?
A) $0
B) $35
C) $490
D) $245
E) $8582

Question

​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by  ,  ,where x is the number of machines used.What is the minimum average cost? ​
A) ​$0 
B) ​$35 
C) ​$490 
D) ​$245 
E) ​$8582

Quizplus · Accepted Answer

To find the minimum average cost, we need to find the minimum value of the function. We can do this by taking the derivative of the function with respect to x and setting it equal to 0.

11ea8970_6a32_1172_861b_b95a96d95d09_TB1301_11

Differentiating with respect to x, we get:

11ea8970_6a32_1173_861b_239554852741_TB1301_11

Setting this equal to 0 and solving for x, we get:

11ea8970_6a32_1173_861b_b5dcf70c867c_TB1301_11

Plugging this value of x into the original function, we get the minimum average cost:

11ea8970_6a32_1172_861b_b95a96d95d09_TB1301_11

Therefore, the minimum average cost is $490, which is answer choice C.

​Average Costs

Average Costs