Question

The cost function of a commodity is `C(x) = 200 + 20x - 1/2x^2` (in rupees). Find the range where AC falls.

Answer 1

`C(x) = 200 + 20x - 1/2x^2`

`\implies AC = 200/x + 20 - 1/2x`

To find AC falls:

`d/dx(AC) = d/dx(200/x + 20 - 1/2x)`

= `-200/x^2 - 1/2`

= `-(200/x^2 + 1/2) < 0, ∀  x > 0`

Hence AC falls continuously.