You need to remember that the derivative of function tells you about the monotony of a function, hence you should find derivative of total cost function such that:
TC'(q) = 60 - 12*2*q + 3q^2
You need to solve the equation TC'(q) = 0 such that:
3q^2 - 24q + 60 = 0
q^2 - 8q + 20 = 0
Notice that the function q^2 - 8q + 20 != 0 for any real value of q, hence the marginal cost given by the function TC'(q) = 3q^2 - 24q + 60 does not reach an extreme for all real values of q.
In reply to 3:
The discussion is about the average cost and NOT the total cost as also mentioned in post 1 reproduced below:
at what level of output is average cost minimum? TC= 60q-12q^2+q^3
Could Sciencesolve please explain how total cost is zero for any production level higher than zero because you have to add the cost of Labour, Materials, Machines and Organization at to manufacture a product?
The discussion is about the average cost which is Total Cost divided by the Total Quantity produced or TC(q)/q or 60-12q+q^2.
For minimum or maximum, the derivative of average cost AC(q) has to be equal to zero or
AC'(q) = -12+2q = 0, that gives q=6
Also 2nd derivative has to be positive in case of minimum cost or AC''(q) > 0, and AC''(q) = 2 in this case.
Hence the level of output at which the average cost is minimum is 6.
The answer to this question is already given by justaguide in link given below:
This, however, does not make a discussion topic where you have only one answer.