Taylor's theorem

Taylor's theorem is a way to understand how a function (in math, a function is a rule that tells you what output you'll get when you put in different inputs) behaves near a certain point. It says that if you look at what a function does at the point you start looking and then look at the changes in the function around the point, the changes can be approximated by a polynomial (a kind of mathematical equation). That means if you want to know what something does close to the start point, you can just look at what the polynomial tells you, instead of working through the whole problem. It's like making a map so you can see where you're going without having to drive all the way there.