微积分the cost of producing x units of a commodity

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微积分the cost of producing x units of a commodity
If C(x) is the cost of producing x units of a commodity,then the average cost per unit is a(x) = C(x)/x.Consider the C(x) given below.Round your answers to the nearest cent.
C(x) = 54,000 + 100x + 4x^(3/2)
Find the production level that will minimize the average cost.
( )units
What is the minimum average cost?
( )dollars per unit

a(x)=C(x)/x=54000/x+100+4x^(1/2)
a'(x)=-54000/(x^2)+2x^(-1/2)=0
x^(3/2)=27000
x=900
900 units will minimize the average cost
a(900)=280
280 dollars per unit is the minimum average cost?

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