6. The relationship between height above the ground (in meters) and time (in seconds) for one of the airplanes in an air show during a 20 second interval can be modelled by 3 polynomial functions as follows: a) in the interval [0. 5) seconds by the function h(t) = 2t4- 8t3- 4t2 + 24t + 435 b) in the interval [5, 12] seconds by the function h(t) = t3 - 1212 - 4t + 900 c) in the interval (12, 20] seconds by the function h(t) = - 6t2 + 140t + 36 n. Use Desmos for help in neatly sketching the graph of the piecewise function h(t) representing the relationship between height and time during the 20 seconds. NOTE: In addition to the general appearance of the graph, make sure you show your work for: 1. points at ends of intervals ii. local minima and maxima interval of increase/ decrease iv. and any particular coordinates obtained by your solutions below. Make sure to label the key points on the graph! b. What is the acceleration when t = 2 seconds? c. When is the plane changing direction from going up to going down and/ or from going down to going up during the first 5 seconds: te [0,5) ?10. 20] s.? . What are the lowest and the highest altitudes of the airplane during the interval e. State an interval when the plane is speeding up while the velocity is decreasing and explain why that is happening. f. State an interval when the plane is slowing down while the velocity is increasing and explain why that is happening. 4. Expalin how you can determine the maximum speed of the plane during the first 4 seconds: te [0,4], and state the determined maximum speed