A firm's total cost is Tc=40+100Q-420Q^2+30Q^3. Find the unit of production at which average variable cost at minimum.

Note that the marginal cost is the derivative of the total cost.

Note that the average variable cost is the integral of the marginal cost over the given interval.

AVC is a minimum when MC = AVC.

A nice video is here:

https://www.youtube.com/watch?v=TBCAHbhhvTg