Question 1187932

The marginal average cost function (MC) is the derivative of the average cost function (AC).


{{{AC(x) = C(x) / x}}}

{{{MC(x) = (d/dx) AC(x)}}}


First, find the average cost function:


{{{AC(x) = C(x) / x}}}

{{{AC(x) = ((5x + 3)(7x + 4)) / x}}}

{{{AC(x) = (35x^2 + 41x + 12) / x}}}

{{{AC(x) = 35x + 41 + 12/x}}}



Now find the marginal average cost function:


{{{MC(x) = (d/dx) AC(x)}}}

{{{MC(x) = 35 - 12/x^2}}}