Question

The total cost function for the production of x units of an item is given by C = 10 - 4x³ + 3x⁴ find the

1. average cost function
2. marginal cost function
3. marginal average cost function.

Answer 1

Given C = 10 - 4x³ + 3x⁴ 

i) Average cost (AC) 

`= "C"/x = (10 - 4x^3 + 3x^4)/x`

`= 10/x - 4x^2 + 3x^3`

ii) Marginal Cost (MC) = `"dC"/"dx"`

`= "d"/"dx" (10 - 4x^3 + 3x^4)`

`= -12x^2 + 12x^3`

iii) Marginal Average Cost (MAC)

`= "d"/"dx" ("AC")`

`= "d"/"dx" (10/x - 4x^2 + 3x^3)`

`= - 10/x^2 - 8x + 9x^2`