# Marginal cost, and minimizing cost & average cost

##### Introduction
###### Lessons
1. Marginal Cost, and Maximizing Cost & Average Cost Overview:
2. Understanding and Minimizing Marginal Cost
3. Understanding and Minimizing Average Cost
##### Examples
###### Lessons
1. Finding & Minimizing the Cost
Given the following information, find the marginal cost and the value of $q$ which minimizes the cost:
1. $C(q)=20+70q^2$
2. $C(q)=250+(1+q) (q-10)^2$
3. The fixed cost is $50000, and the cost to make each unit is$500
4. The fixed cost is $25000, and the variable cost is$200$q^2$.
2. Finding & Minimizing the Average Cost
Given the following information, find the marginal average cost and the value of $q$ which minimizes the average cost:
1. $C(q)=q^4-2q^2+10q$
2. $C(q)=100+q^2$
3. $C(q)=q^3-4q^2+10q$
4. $C(q)=2q$
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###### Topic 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:

$AC'(q)=0$