Section 3.6 Problem number 1 14 were doing a graphic exploration here. So what they give us is sort of fairly complicated. Here is a trick function, okay? And this trick function sort of a trick polynomial. If he were, there's a really good job of estimating the salt to function. And what they wanted to do is to do an exploration on that. So I've got assaulted function, which is this piece wise linear function. Okay, which you see, um, all graft there. Um, and what they want me to do is to say Okay, well, how well does this trick polynomial? Approximate that. And what you can see is pretty good. So if you look at it, um, you see, it has troubles right there at the turns, So it has a little bit of trouble every time there's a sharp corner, But otherwise, you can see this trick polynomial. You know, it's weaving a little bit, but it's sort of hard to tell. So that's a fairly good approximation when we look at what's going on here. So from, um, negative pie, too. Hi. And that should be a should be good. So that's a good approximation. So what they want us to do is to find the derivative of this function. So I went ahead and wrote it out. But really, I mean, it's how do you differentiate co sign you get a minus sign, and then you're gonna have to in front of it. So really, you see the pattern It's taking this expression that you see right here making it positive, putting a two in front, changing the co signed to sign, same thing putting the six in front, making it positive and changing the co sign to a science that this would be the derivative function that we see showing up. So now let's see what would be the derivatives. I want to take this function off. What would be the derivative of this function? Okay, if you look at this solitude function, um, it's going to be, you know, the slope is gonna be one on this first piece. Negative 11 and negative one. So what does the derivative look like? The derivative is just gonna oscillated between these values. So this is what the derivative of the salt to function looks like. OK, so it's gonna be, um oscillating between one and negative one and it's gonna be undefined these corners. Now I graphed the trigonometry trick in a metric polynomial. What would its derivative look like? And that's what you see here. So in this case, I'm looking at okay, When I graphed the derivative of this polynomial, I'm seeing that OK, things air sort of quite different. So my trick polynomial was pretty good in estimating the, um the function, but pretty bad when it comes to estimating the derivative will follow up on this in the next problem. So again, the overall consensus was I could use thes trick Modelo meals pretty well for estimating this salt to function. And it appeared to have troubles that it appeared to have troubles at the points that they're gonna be discontinuities in the derivatives. So it was a pretty good approximation, except for those points where that would happen. OK,