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.
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)
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)]
C’(500) = ~0.4025