Discussion Topic In this unit you discovered how graphs of p

Discussion Topic In this unit, you discovered how graphs of polynomial functions can be used to model and design roller coasters. Imagine a roller coaster, or look for a photo of one online, and think about its design. Discuss where the modeling concepts you learned for designing a roller coaster break down and are not sufficient for capturing the roller coaster that you\'re analyzing. In particular, discuss the mathematical concepts from this unit related to graphing polynomials, determining maximum and minimum values, and finding points where a function crosses an axis.

Solution

In particular, when you get right up to the top of the roller coaster just before you are going to go plummeting down to the bottom. I also like that point at the bottom where you are suddenly pulled back up, and your innards go all the way down to your feet.Let us see if we can analyze a roller coaster. Let us take its position across the Earth as x and its height as y. So let us draw out the roller coaster height as a function of its location, x. the point at the top and the point at the bottom of this roller coaster function. These points are called extrema. Extrema are extreme values, like a maximum or a minimum value. On a roller coaster, on this particular roller coaster, there is a maximum height, so it is a maximum y value, and there is a minimum height, a minimum y value. If I ignore the rest of the graph, that is a maximum value. Extrema can be global, or what we call absolute extrema. This is a maximum or a minimum value for the entire domain. That is the very top of the roller coaster and the very bottom of the roller coaster. But you can also have local extrema. We also call them relative extrema, and these are the maximum or minimum values in a small region. So going back to my roller coaster, I have the global maximum and the global minimum, as well as local maximum and local minimum places. You can think of these kind of like mountain ranges and valleys. If we take y =0. we get a point crosses to the x-axis and if we take x=0, we get a point crosses to the y-axis.