Help with my AP Calculus Final Project please and thanks! If you are willing to complete it please let me know and I can split it up into several questions and give good ratings for all of them because I understand its alot of work. It doesn't have to be anything fancy, just the bare minimum to fill out the rubric.

Final Project - AP Calculus AB Objective: You have been hired by six flags to design their next greatest roller coaster. You will be using what you know about continuity, differentiability, functions, and other Calculus Six Flags topics to create a plan for a roller coaster that is both safe and exciting. Directions: Your goal is to develop a roller coaster made up of a piecewise function that consists of at least five different functions. To ensure safety, the roller coaster must be continuous and differentiable at all points. You can complete this individually or in pairs (only one product needs to be submitted). Note: x will represent the horizontal displacement and y will represent the height of the car (both in feet). There are a few regulations that the roller coaster must meet to be approved by Six Flags. The roller coaster needs to end at the same height it starts at. You can add a platform (horizontal line) but that will not count as one of your five functions. It must be at least 200 feet in length. The roller coaster can only go underground once since there is only enough money in the budget for one tunnel (height can be negative only once). It can have a maximum height of 250 feet. It must have at least one drop and/or loop. It must consist of at least three different types of functions we have learned about this year - linear, quadratic, polynomial, radical, exponential, logarithmic, trigonometric. o Linear - y = ax + b Logarithmic - y = log. x + b o Quadratic - y = ax' + bx + c Sin - y = a . sin(x + b) - c o Polynomials - y = ax + bx* + ex + d o Cos - y = a . cos(x + b) - c o Radical - y = avx+ b+c Exponential - y = a(b)* + cYour final product must consist of the following 3 parts. All parts below can be hand- Reflection Questions: written and/or typed and then handed in or shared with me virtually. 1. Use what you know about derivatives to find the critical points of your roller coaster. You may use a calculator to find the x-values, but show the equation/explain the Proof that the function is continuous and differentiable on all points (focus on steps you used. On what intervals(s) is the roller coaster increasing? where the function changes) Ex: f(x) = avx -b+c 25