Let's see if we can give ourselves an intuitive understanding of the mean value theorem. And as we'll see, once you parse some of the mathematical lingo and notation, it's actually a quite intuitive theorem. And so let's just think about some function f. So let's say I have some function f, and we know a few things about this function. We know that it is continuous over the closed interval between x equals a and x is equal to b. And so when we put these brackets here, that just means closed interval. That means we're including, so when I put a bracket here, that means we're including the point a. And if I put the bracket on the right-hand side instead of a parenthesis, that means that we are including the point b.