so if you know if we're looking at this and obviously let's just pretend this is a roller coaster it'd be an absolute horrible roller coaster because you can see there's a cusp in the roller coaster and that'd be probably kind of difficult to kind of ride on right probably pretty jerky but if we're talking about the maximum everybody usually wants to talk about the max and saying hey you know how high is that roller coaster go right but if we kind of and we think about the global terms that's why we call it global think about like a big picture right and you can see that the you know the global max is right here the global man is right down there however if we were to kind of like zoom in and that's the way i kind of think about it like kind of look at instead of the global we kind of look at the local look at something a little bit smaller so if we zoom in at a couple different areas we see that there's different max amines right if you were to only if i was only to draw a picture of what's in that box you would say oh well that's a maximum that's a minimum that's a minimum and that's a maximum once you agree if you're just looking at what was inside the box right because any point to the left and to the right is smaller than that point any point to the left and right is higher than that points and the same thing just falls with all the other logic right so when i say you know max and min you can assume that we're talking about the global max and global min but i also want you guys to open up that we are going to also be talking about relative min and relative max so again this is g of x so we call that the relative or the local min and we could say that that relative local min occurs at g of c and g of e oh of sorry of g and g g of c and g of e at x equals c and x equals e so would you guys agree those we're talking about the global the minimum but then also where those values occur yes okay and then we could say g of x has a relative max and a relative min of i'm sorry relative max what was this g of d uh no sorry relative minute g of b of g of b and g of f at x equals b and x equals f okay now we're talking about the relative min and the relative max what we're it's the exact same thing like the reason why this is a maximum is because that g of b is greater than equal to g of x on a given interval and now like what would that interval be you could say that interval is like between a and c right won't you guys agree with me like so as long as it's on any given interval a lot of times we just call it interval i because if you have an interval and you could say that like that value is like your max is your absolute maximum in that interval then it's a relative max or min and like for example you could just say like from a you know to c which is going to be producing your uh your relative uh relative maximum and that's going to be occur like the same thing for g of e we could say that you know g of e is less than or equal to g of x on the integral you know i which is let's say from d to f you know so if you can determine an interval and that value is the lowest term then that's important now the next thing i want you guys to look at which is a really really really