PART B: a) One of the submissions for the roller coaster proposal contains the following information: . " The function representing the roller coaster is y=-x² + 2x³ + 13x² - 14x - 24. Two of the x-intercepts are at x = -3 and x = 4. Determine the other x-intercept(s) Determine the first derivative of the function There are three extrema at x -2.193 x 0.5, and x 3.193. Determine the y-values at the extrema. (round the answer to the nearest hundredth) Determine the first derivative of the function There are two possible point of inflection at x =-1.055 and x = 2.055. Determine the y-values at the points of inflection. (round the answer to the nearest hundredth) Use a chart, to complete the first and second derivative tests in the chart below to get a better idea of what the roller coaster would look like. The sign of the FIRST derivative The behaviour of the function The sign of the SECOND derivative The behaviour of the function The SHAPE of the graph b) Draw a sketch of the roller coaster on a graph (from the previous chart). Be sure to graph all necessary points, label your Critical Points (CPs) and Points of Inflections (POIs) and indicate them on the graph. Choose an appropriate scale for graph.