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'?  

Answer 1

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_A is decreasing if `"dC"_"A"/"dx" < 0`

i.e. 2x - 16 < 0 

i.e. 2x < 16 

i.e. x < 8

∴ Average cost C_A is decreasing for x < 8.