Marginal cost, and minimizing cost & average cost - Derivative Applications

Notes:

Marginal Cost (MC) is the additional cost that is gained when you increase the unit by one. It is also the derivative of the cost function. In other words,

$MC=C'(q)$

Average Cost (AC) is the amount of cost generated per unit. In other words,

$AC(q)=\frac{C(q)}{q}$
In this section, we would want to find the quantity $q$, which minimizes cost and average cost. To minimize cost, we would want to solve for:

$MC=0$

To minimize average cost, we would want to solve for:

$AC'(q)=0$