# 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. $C(q)=2q$
###### Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
• #### Easily See Your Progress We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
• #### Make Use of Our Learning Aids   ###### Practice Accuracy

See how well your practice sessions are going over time.

Stay on track with our daily recommendations.

• #### Earn Achievements as You Learn   Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
• #### Create and Customize Your Avatar   Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
###### 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:

$AC'(q)=0$