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Question
The cost C of producing x articles is given as C = x3-16x2 + 47x. For what values of x, with the average cost is decreasing'?
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Solution
C = x3 - 16x2 + 47x.
Average cost CA = `"C"/"x" = ("x"^3 - 16"x"^2 + 47"x")/"x"`
∴ CA = x2 - 16x + 47
Differentiating w.r.t. x
`"dC"_"A"/"dx" = 2"x" - 16`
CA is decreasing if `"dC"_"A"/"dx" < 0`
i.e. 2x - 16 < 0
i.e. 2x < 16
i.e. x < 8
∴ Average cost CA is decreasing for x < 8.
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