methods question

:)

I have been asked to create a roller coaster. The first function needs to be a polynomial with 6 stationary points at horizontal distances of 8m, 12m, 28m, 32m and 40m. I need to start by creating the derivative. Could someone please give me some pointers of how to do this.

Thanks

S200

Given that the points need to be stationary, you are looking for a Polynomial where the integral is zero at the points you have mentioned. the fact that it has 6 stationary points and only 5 other points are mentioned leads me to believe that it should probably start and end at zero on the y-axis.