Answer:
The average cost function is [tex]\bar{C}(x)=6+\frac{3100}{x}[/tex].
The marginal average cost function is [tex]\frac{d}{dx} \bar{C}(x)=-\frac{3100}{x^2}[/tex].
Step-by-step explanation:
If [tex]C(x)[/tex] is the cost function for some item then the average cost function is,
[tex]\bar{C}(x)=\frac{C(x)}{x}[/tex]
The marginal average cost function is the derivative of the average cost function.
We have that the total weekly cost function is
[tex]C(x) = 3100 + 6x[/tex]
Applying the above definitions, we get that:
The average cost function is
[tex]\bar{C}(x)=\frac{3100 + 6x}{x} =6+\frac{3100}{x}[/tex]
The marginal average cost function is
[tex]\frac{d}{dx} \bar{C}(x)=\frac{d}{dx}(6+\frac{3100}{x})\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dx} \bar{C}(x)=\frac{d}{dx}\left(6\right)+\frac{d}{dx}\left(\frac{3100}{x}\right)\\\\\frac{d}{dx} \bar{C}(x)=0-\frac{3100}{x^2}\\\\\frac{d}{dx} \bar{C}(x)=-\frac{3100}{x^2}[/tex]
