*PART TWO OF THE FIRST QUESTION* You created two roller coasters, the second one comes with the given:

For the first 10 seconds of the ride, the height of the roller coaster can be determined by , where t is the time in seconds and h is the height in feet. Answer the following questions as part of your investigation.

1- Classify this polynomial by degree and by number of terms.

2- Clearly describe the end behavior of this function and the reason for this behavior in terms of f(x) and x.

3- Graph the polynomial function for the height of the roller coaster.

Color the graph blue where the polynomial is increasing and red where the polynomial is decreasing. Identify increasing and decreasing intervals.

4- find approximate relative maxima and minima of this function. Round your answers to ONE decimal places.

5- Find the height of the coaster when t = 3 seconds and 7 seconds.

Suppose that this coaster is a 2-minute ride.

6- Do you think that h(t)=-0.2t^4+4t^3-24t^2+40t+4 is a good model for the height of the coaster throughout the ride? Clearly explain and justify your response.