SOLUTION: 10. The total cost to produce x units of paint is C(x) = (5x + 3) (7x + 4). Find the marginal average cost function.

Algebra ->  Test -> SOLUTION: 10. The total cost to produce x units of paint is C(x) = (5x + 3) (7x + 4). Find the marginal average cost function.      Log On


   

Question 1187932: 10. The total cost to produce x units of paint is C(x) = (5x + 3) (7x + 4). Find the marginal average cost function.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

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

AC%28x%29+=+C%28x%29+%2F+x
MC%28x%29+=+%28d%2Fdx%29+AC%28x%29

First, find the average cost function:

AC%28x%29+=+C%28x%29+%2F+x
AC%28x%29+=+%28%285x+%2B+3%29%287x+%2B+4%29%29+%2F+x
AC%28x%29+=+%2835x%5E2+%2B+41x+%2B+12%29+%2F+x
AC%28x%29+=+35x+%2B+41+%2B+12%2Fx


Now find the marginal average cost function:

MC%28x%29+=+%28d%2Fdx%29+AC%28x%29
MC%28x%29+=+35+-+12%2Fx%5E2