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

The instantaneous rate of change of the average cost function is given by its derivative. Taking the derivative of the average cost function gives:

A'(x) = (11,800/x^2) - 40

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

0 = (11,800/x^2) - 40
    40x^2 = 11,800
    x^2 = 295
    x = sqrt(295) = 17.15 (rounded to two decimal places)

Therefore, the level of production where the instantaneous rate of change of the average cost equals zero is approximately 17.15 units. The correct choice is C.

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