A men's suit manufacturer finds that the cost, in dollars, of producing x suits is given by C(x) = 841 + 18x^1/2

decimal-places
average-cost

#1

A men’s suit manufacturer finds that the cost, in dollars, of producing x suits is given by C(x) = 841 + 18x^1/2. Find the rate at which the average cost is changing when 500 suits have been produced. Round the answer to four decimal places.

Answer:

To find the rate of change of an equation you will take the derivative of the equation. So,
C’(x) = (1/2)*18x^(1/2-1)
simplified:
C’(x) = 9x^(-1/2)

To find the rate of change at suit 500, you will just plug in 500 for x and get
C’(500) = 9[500)^(-1/2)]
simplified:
C’(500) = ~0.4025