Math 205 Lecture 13a - Linear Approximation and Marginal Analysis part 1

Welcome to lecture 13a of Math 205 - Elements of Calculus.

We had technical difficulties today. So this lecture is split in two parts, lecture 13a and 13b. I don't think we missed a lot of material, but we missed most of an awesome classroom discussion when we conceptually applied what we learned to some real world examples. Bummer. I'm sorry. Anyway...

In this lecture, we actually begin by going over the last quiz given to the class, but then we jump into linear approximation, where we use the tangent line of a function at a point to approximate the value of the function at another point close by. We show how to do this, and discuss why it's an important and widely useful application of calculus and the tangent line.

Afterwards, we extend the idea of using the derivative for marginal analysis. Which approximates how a function will change in the future given that we know how it is behaving right now. In one instance, we apply this to cost, to judge how much it would cost to produce one more product given that we've already produced a certain amount of products.