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### Course: Differential Calculus>Unit 4

Lesson 3: Non-motion applications of derivatives

# Marginal cost & differential calculus

Through the lens of economics, we examine how the derivative can be used as a tool to understand marginal cost. We'll use a factory scenario to see how cost changes with quantity, and how this insight informs production decisions. Calculus—in real life! Created by Sal Khan.

## Want to join the conversation?

• what is this "margin" Sal talks about?
• The amount that total costs increase per each additional unit of good produced, which is why it changes as you move right on the x-axis.
• How likely is it that something like cost can be modeled fairly accurately by an algebraic function?
• It tends to be fairly likely. Lets say your expenses that need to be covered are: worker payment, product materials, machine time, and building rent.
Worker payment, and building rent are fixed, lets say 2000, for worker payment, and 1000 for building rent.
Lets also say that product materials cost half of the price of the product (25 * the number of products), and that running the machine costs 1/10 the number of products squared (5 * products ^2).
This can be written as: `cost(#products) = 1/10*5(#products)^2 + 1/2*25(#products) + 3000`
• can you explain why the cost of production increases as the quantity increases? why is this graph an upward sloping curve?
• Is finding C'(q) or the marginal cost of a such a function used for anything in economics except for finding when to stop producing something?
• its also used to calculate the amount of a certain that is supplied by all firms in the economy at any given price, which is supply. supply can be used to calculate supply curves to construct other economic models, usually a supply and demand model.
• Are there similar videos available for the application of integrals?
• When we use derivative it provides instantaneous rate of change, suppose we calculate marginal cost using derivatives at quantity 5 it will provide additional cost of very small change(near zero) in quantity ,how can we use that for change in a complete unit? for example can we use it for for estimating complete additional 1 unit of quantity?why?
• It's assuming the rate is not going to drastically change very quickly, of course the more you try and predict ahead the more inaccurate the precition will be from that point. There are actually a few instances of this kind of using the trend to predict things nearby in calculus.