The total cost function for a commodity is given by c=4x-6x^2+3x^3.
Find the value of the output x for which the average cost is the loswest.
To find the value of x for which the average cost is lowest, we need to find the value of x at which the derivative of the total cost function (c) with respect to x is equal to zero.
The derivative of c with respect to x is:
c' = 4 - 12x + 9x^2
Setting c' equal to zero and solving for x:
4 - 12x + 9x^2 = 0
Rearranging the equation:
9x^2 - 12x + 4 = 0
Using the quadratic formula:
x = (-(-12) ± sqrt((-12)^2 - 4*9*4)) / (2*9)
Simplifying:
x = (12 ± sqrt(144 - 144)) / 18
x = (12 ± sqrt(0)) / 18
x = 12 / 18
Therefore, x = 2/3.
So, the value of the output x for which the average cost is lowest is 2/3.