The Project Consider the design of a car race track. The race track might look like an ellipse but it might also have some other sharp turns, like a cubic function. If a drive does not slow down enough before entering each turn, the car may slide off the racetrack. If the driver loses control completely, the car may fly off the track entirely on a path tangent to the curve of the racetrack. 1. Suppose you are designing a new race track. Once section of the track can be modeled by the function f (x) = x3 3x2 x. The current plan calls for grandstands to be built along the first straightaway and around a portion of the first curve. The plans call for the front corner of the grandstand to be located at the point (1.9, 2.8). Graph this function and the planned location of the grandstands. 2. We have determined that drivers are most likely to lose control of their cars as they are coming into a turn, at the point where the slope of the tangent line is 1. Find the (x, y) coordinates of this point near the turn. 3. Find the equation of the