This is not a project and/or assignment for marks, as this is a textbook question, and will not be copying the tutors work. Since the purpose of this is to increase my knowledge and understanding in the topic, and to aid me a bit in the viewing of how they are connected. Follow the instructions and guidelines to complete the activity. Answer the questions that correspond to the activity, and when done with the desmos roller coster, please share the link, all references are in the images below.

Piece-wise 6+ functions that start/finish at same height with first hill Components as highest. Tech. Doc. Calculations Correct algebraic derivatives (1st, 2nd of each piece of the function). Tech. Doc. Max/Min Correct max/min height of each piece of the function has Height Calculations been calculated algebraically as well as overall max/min height. Tech. Doc. Max/Min Correct max/min velocity of each piece of the function has Velocity Calculations been calculated algebraically as well as overall max/min height. Piece-wise Function Creative, unique, and "record-breaking". Overall function appears continuous and differentiable. Graph Plot h(t) Piece-wise function is clearly plotted in graphing program with function labelled as well as important features (overall max/min). Axis is labelled. Graph Plot v(t) and a(t) Piece-wise functions are clearly plotted in graphing program with functions labelled as well as important features (overall max/min). Axis is labelled. Poster Visually stunning. Sells the rollercoaster by highlighting all the main features. Grammatically correct with clear explanations. Mathematical Form Correct use of mathematical symbols, units, conventions, and labels. All calculations shown. Overall impact Overall roller coaster is unique and realistic.A consortium of math aficionados have decided to open a math-themed amusement park in Toronto. The crown jewel in the park's design will be a roller coaster called "Leibniz's Dragon". Named for the 17"-century German philosopher and mathematician, Gottfried Leibniz, the Dragon needs to be as fun, exciting, and scary as calculus. The consortium has decided to open the design contest to the public, and you have decided to enter a record breaking design to the contest. Task: design and sell a roller coaster to the judging committee. Guidelines: 1. You must use a graphing program (ex. DESMOS* ) to create a piecewise function consisting of at least six parts (of the piecewise function) that will define h(t), height in terms of time. You need to create another piecewise graph of its derivative. You also need to create another piecewise graph of its second derivative. To guarantee an exciting ride, you must use each of the following types of functions at least once: quadratic, cubic, sinusoidal, and exponential/logarithmic. a. Your roller coaster must complete a full circuit every time it runs, and as such, it needs to start and finish at the same height. b. The function, h(t), must be continuous, and appear to be differentiable, at a glance. c. As with any roller coaster, once it's going, it should stay going without needing to be hauled up to the top of a hill. For this reason, your tallest hill should be the first one the coaster reaches. *If you decide to use DESMOS, make a DESMOS account so your graphs are SAVED! 2. You must create a presentation board (like Task 1's poster) to sell your design, as well as an accompanying technical document. a. The presentation board should highlight the main features of your design and is designed to catch the eye. b. The technical document is where your mathematical justification goes. For example, if one of the features that you use to sell your coaster is its maximum speed, then the calculations that you do to find the maximum speed should be included in the technical document. c. Your technical document must include a minimum list of features of your coaster: Consult the following Checklist. Checklist: . Piecewise Function . Proof of the function's continuity . Derivatives of each piece of the function . Second derivatives of each piece of the function . Maximum and minimum height of each piece . Overall maximum and minimum height . Maximum and minimum velocity of each piece . Overall maximum and minimum velocity