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'?

The Cost C of Producing X Articles is Given as C=X3-16x2+47x. - Mathematics and Statistics

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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'?

C = x³ - 16x²+ 47x.

Average cost C_A = `"C"/"x" = ("x"^3 - 16"x"^2 + 47"x")/"x"`

∴ C_A = x² - 16x + 47

Differentiating w.r.t. x

`"dC"_"A"/"dx" = 2"x" - 16`

C_Ais decreasing if `"dC"_"A"/"dx" < 0`

i.e. 2x - 16 < 0

i.e. 2x < 16

i.e. x < 8

∴ Average cost C_Ais decreasing for x < 8.

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