Question

The cost, in dollars, of producing x belts is given by C(x) = 634 + 18x - 0.071 x^2. Find the rate at which average cost is changing when 324 belts have been produced. When 324 belts have been produced, the average cost is changing at_______ for each additional belt.

Answer 1

When 324 belts have been produced, the average cost is changing at -28 dollars for each additional belt.

Explanation:

The cost of producing x belts is given by:

`C(x) = 634 + 18x - 0.071x^(2)`

Find the rate at which average cost is changing when 324 belts have been produced.

This is
`C'(324)`. So

`C(x) = 634 + 18x - 0.071x^(2)`

`C'(x) = -0.142x + 18`

`C'(324) = -28`

So the correct answer is:

When 324 belts have been produced, the average cost is changing at -28 dollars for each additional belt.