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

Answer:

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

Step-by-step 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.