Suppose that the total cost function, in dollars, for a certain commodity is given by , where x is the number of units produced. The average cost is given by for any level of production. Find the level of production where the instantaneous rate of change of the average cost equals zero. Round your answer to two decimal places.

Question

Suppose that the total cost function, in dollars, for a certain commodity is given by  , where x is the number of units produced. The average cost is given by  for any level of production. Find the level of production where the instantaneous rate of change of the average cost equals zero. Round your answer to two decimal places. ​

Quizplus · Accepted Answer

We know that instantaneous rate of change of the average cost is given by the derivative of the average cost function. So we need to find where the derivative of the average cost function equals zero.

Taking the derivative of the average cost function, we get:

11ea984b_aca0_09c8_9029_056172c7ebdd_TB4005_11

Simplifying, we get:

11ea984b_aca0_09c9_9029_5fb5fc2014fd_TB4005_11

Setting this equal to zero and solving for x:

11ea984b_aca0_7efb_9029_9baef55d5b4b_TB4005_11

Rounding to two decimal places, we get x = 2.50.

Therefore, the level of production where the instantaneous rate of change of the average cost equals zero is 2.50 units, which is choice C.

Suppose That the Total Cost Function, in Dollars, for a Certain