Calculus12---Roller Coaster -- with Differentiation, Continuity.

1. make a roller coaster function using www.desmos.com. the function should be a piecewise function with 3 or more pieces. the roller coaster should have just 2 dimensions.

2. draw a graph of the piecewise function on poster paper and label the graph. write a proof to show that the function is continuous and differentiable at the connecting points.

(It would be great if several sentences are used to help describe the roller coaster, as well as the function and the calculations.)