Answer:
[tex]C(x)=0.01x^{3} +0.2x^{2} +20x +110[/tex]
Average cost:
[tex]\frac{C(x)}{x}=\frac{0.01x^{3} +0.2x^{2} +20x +110}{x}[/tex]
[tex]=0.01x^{2} +0.2x+20+\frac{110}{x}[/tex]
Average cost at x = 1,000
[tex]=0.01(1,000)^{2} +0.2\times1,000+20+\frac{110}{1,000}[/tex]
= 10,220.11
[tex]Marginal\ cost=\frac{dC(x)}{dx}[/tex]
[tex]= 0.03x^{2} +0.4x+20[/tex]
Marginal cost at x = 1,000
[tex]= 0.03(1,000)^{2} +0.4\times1,000+20[/tex]
= 30,420
Since marginal cost is greater than the average cost, the average cost is increasing.