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. Over what interval in the domain do average costs increase?

Question

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. Over what interval in the domain do average costs increase? ​

Quizplus · Accepted Answer

To find where the average costs increase, we need to find the intervals where the derivative of the cost function is positive. Taking the derivative of average costs with respect to x, we get: 11ea984b_b219_8d91_9029_804561de2596_TB4005_11 Since 2x is always positive, the sign of the derivative depends on the sign of (20-2x) which is negative for x>10 and positive for x<10. Therefore, the average costs increase for x in the interval 0 < x < 10, and decrease for x in the interval x > 10. Thus, the answer is (B) 11ea984b_b219_6893_9029_a9425e08da10_TB4005_11.

Suppose the Average Costs of a Mining Operation Depend on the Number