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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.
Solution
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
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