Algebra question

Question

an aircraft factory manufactures airplane engines. the unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. if x engines are made, then the unit cost is given by the function C(x)=x^2-360x+44,597. what is the minimum unit cost?

do not round your answer

Answer 1

take the derivative and set = 0 solve for x

C'(x) = 2x -360 = 0

x = 180 engines

C(180) = (180)^2 -360(180) + 44,597 = 44,597 - 32400 = $12,197 = minimum cost

Answer 2

C'(x) = 2x -360 = 0

x = 180 engines

C(180) = (180)^2 -360(180) + 44,597 = 44,597 - 32400 = $12,197 = minimum cost