Determine the open intervals on which the graph of the function is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) y = -x3 + 9x2 - 2 concave upward concave downward

At x=3 the function, in the graph belowe is -2 +234 | 2 A. Continuious and differentable B. Not continous and differentable c Continais and not difforentable D. Not continous and not differentalle

State the end behavior and y- intercept of the function given. Do not graph 1. F(x) = x³ + 6x² – 5x – 2, hint set x=0 to find the y-intercept

+ 3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine function. The high and low points of this part differ by 24 meters and cover a horizontal distance of 40 meters from the high point to the low point. The low point is 6 meters below ground in a tunnel. Let y repre- sent the number of meters the track is above or below ground, and let x repre- sent the number of meters the track is horizontally from the high point. a. Sketch this situation. b. The equation y = 12 cos (4.5x) + 6 models the situation when x and y are in meters and 4.5 is in degrees per meter. Rewrite y = 12 cos (4.5x) + 6 as an equation for which the coefficient of x is in radians per meter. c. What is the length of a vertical support girder at the high point? At a dis- tance of 6 meters horizontally from the high point? At a distance of 20 meters horizontally from the high point? d. Measured horizontally, how far from the high point does the roller coaster enter the…