2. A flight from Frankfurt, Germany to Washington DC takes off at 6am and lands after 8 hours. During the flight, the plane travels 4000 miles. Note that you may assume the functions modeling the vertical and horizontal positions/speeds of the plane are differentiable, and Frankfurt and Washington are both a sea level. (a) Can we guarantee that the plane achieves a horizontal speed of 500 mph (miles per hour) at some point in time over the course of its flight? Justify your answer using a theorem. (b) Can we guarantee that the plane is flying at constant altitude at some point over the course of its flight? Justify your answer using a theorem. (c) Explain why there are at least two times during the flight when the speed of the plane is 400 miles per hour. Justify your answer using a theorem. Hint: What is the initial speed of the plane? What is the plane's speed when it lands?