Average cost and marginal average cost function

Question

Consider the average cost function c(x)=0.000002x^3 - 0.03x^2 + 400x + 80,000

a. Find the average cost function c̅ associated with the

total cost function c.

b. What is the marginal average cost function c̅'?

c. Compute c̅' (5000) and c̅' (10,000), and interpret

your results.

d. Sketch the graph of c̅. (Please show the steps of how to graph the function because this is the question I’m specifically confused about)

Answer 1

a) c̅ = c(x) / x

Thus, c̅ = (0.000002x^3 / x) - (0.03x^2 / x) + (400x / x) + (80,000 / x)

c̅ = 0.000002x^2 - 0.03x + 400 + (80,000 / x)

b) Take the derivative of the average cost function.

Use power rule:

c̅' = 0.000004x - 0.03 - (80,000/x^2)

c) c̅' (5000) = - 0.132 - > Plug 5000 into your marginal average cost function c̅' .

c̅' (10,000) = 0.0092 - > Plug 10,000 into your marginal average cost function c̅' .

d) It is hard to help you with that just by typing, I suggest you watch some youtube videos for this.