math
posted by Britney on .
Suppose the total cost function for manufacturing a certain product C(x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize the average cost. (Round your answer to the nearest whole number.)
C(x)=0.2(0.01x^2+133)
? units

average cost = totalcost/number of units
a(x) = C(x)/x
= 0.2(0.01x + 133/x)
minimum avg cost is where a'(x) = 0
a'(x) = .02(.01  133/x^2)
x = 10√133 = 115.3, so 115