Question

A company's total cost C(x) to manufacture a quality x of a certain item can be represented by C(x) = 0.03x^2 + 27x + 850. Find the average rate of change for the first 300 items manufactured.

Answer 1

The average rate of change for the first 300 items manufactured is 9.

Step-by-step explanation:

The average rate of change for the first 300 items manufactured can be found by calculating the change in the total cost divided by the change in the quantity produced. In this case, the total cost function is given by C(x) = 0.03x^2 + 27x + 850. To find the average rate of change, we need to calculate the total cost for 300 items and subtract the total cost for 0 items, then divide the result by 300.

So, C(300) - C(0) = (0.03(300)^2 + 27(300) + 850) - (0.03(0)^2 + 27(0) + 850).

Simplifying the equation:

C(300) - C(0) = 2700

The average rate of change for the first 300 items manufactured is 2700/300 = 9.