A firms cost function for product x is AC=1/3q^3-100q-30?

Question:at what level of production of x will the AC be minimized?

Answers:
Let y = 1/3q^3 -100q -30

At the minima dy/dx = 0

dy/dx = q^2-100 = 0

q = 10
( q can be -10 too, but negative units is not possible)
10.
If you don't want to learn algebra, use excel for these types of problems. Type this into excel with "q" being a reference to another cell. For example, type "=1/3*A1^3-100*A1-30". Type any number into cell A1. Go to Tools and select Solver. Ask it to minimize the value of the cell that you typed the formula into by changing the value in A1.

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