>> Well, let's evaluate it according to this function. F of X plus delta X means in the F function. Replace X with X plus delta X. So this X is replaced with X plus delta X. So it's binomial squared minus 6 times binomial. All right. Let's go down here. Binomial squared minus 6 times binomial plus 11. All right, this is that. Okay? Now, minus F of X means minus this. So minus X squared minus 6X plus 11. All right? And then bring down delta X for the denominator. Let's expand further. We have X plus delta X squared. X squared plus 2 times the product. Two times X, delta X. Then delta X squared. Then minus 6X. Minus 6 times delta X. And then the negative of all of this, the sines change and you bring down everything. Now, when you do the algebra on this it kind of looks complicated because it's just strung out. It's not hard. It's just that it's strung out. So all you need to do is create a lot of space left and right when you do these. And you're going to have to do these several times, okay, as part of your homework. But just give yourself a lot of room and write legibly. And the nice thing about these is that there are a lot of cancellation opportunities. Once you get the expansion complete then all of the terms that don't involve delta X turn out to go out. That is, this X squared. Now, follow me way over here. This X squared cancels with this minus X squared. Okay? So those go out. And this minus 6X and plus 6X go out. And this plus 11 minus 11 go out. And now the only terms remaining are terms that involve delta X. Well, if all of these terms remaining involve delta X, I'm going to factor that delta X out of those terms as I bring them down. And I'm going to use this term of sort of highest degree first. I have delta X squared. When I take a delta X out as a factor, I'm left with the other delta X [inaudible] factor. When I take delta X out of this term I'm left with 2X. When I take delta X out of this term I'm left with minus 6. And now I have the delta X in the denominator, so these guys cancel. And now I have evaluated that difference quotient and I get this.