Question

The average cost function associated with producing and marketing x units of an item is given by AC = 2x – 11 + `50/x`. Find the range of values of the output x, for which AC is increasing.

Answer 1

AC increases when `"d"/"dx"`(AC) > 0

C = 2x - 11 + `50/x`

`"dC"/"dx" = 2 - 0 + 50 ((-1)/x^2)`

`= 2 - 50/x^2`

`"d"/"dx"`(AC) > 0

`2 - 50/x^2` > 0

`2 > 50/x^2`

2x² > 50

x² > 25

x > 5