What is the minimum possible cost per unit?

Question

The cost per unit, C(x), when manufacturing X units is given by the formula:

C(x)=2x^2-24x+76

What is the minimum possible cost per unit?

Answer 1

take the derivative and set equal to zero

C'(x) = 4x -24 = 0

4x=24

x = 24/4 = 6

plug x back into the cost function

C(6) = 2(36) -24(6) + 76 = 72 -144 + 76 = 4 per unit is the minimum average cost