1. Given the function M(t) = 21 - 31- - 36t, find the critical values and determine, using both the second derivative test and a sign chart, the nature of these critical values. 2. A projectile is launched with a velocity of 27 m/s at 55 to the ground. Determine its horizontal and vertical velocities. 550 3. Two trains start from the same point at the same time, one going east at a rate of 40 km/h and the other going south at 60 km/h, as shown in the diagram at right. Find the rate at which they are separating after 1 h of travel. Train A 40 km/h . . . . . . ...... Train B 60 km/h Distance Between Trains 4. A professional basketball team plays in a stadium that holds 23,000 spectators. With ticket prices at $60, the average attendance had been 18,000. When ticket prices were lowered to $55, the average attendance rose to 20,000. Based on this pattern, how should ticket prices be set to maximize ticket revenue? 5. Higher-order derivatives are derivatives that are taken found after a previous derivative has been taken. For example, we can take the first derivative (y') and the second derivative (y") and the 3rd derivative (y") if we are given the original function (y). Quite often, multiple higher-order derivatives can be found. Higher- order derivatives are used in Science (physics) and mathematics (Differential Equations). A differential equation is an equation that contains functions and some higher-order derivatives. Using a formal proof structure (LHS = RHS), prove the differential equation xy' - 3y + y" +4 =2x2 given the function y = x3 - 2x2 + 3x