1. The position function of a particle is given by s(t) = 2t^3 + 4t^2 - t, where time, t, is in seconds and distance, s, is in metres. At t = 1 seconds, is the particle speeding up or slowing down? Give a reason for your answer. 2. Given y = 4(u^3) - u and u = sqrt x, a) Determine dy/dx at x = 9 using the Leibniz form of the chain rule. b) Determinedy/dx at x = 9 by first rewriting the question using only variables x and y. 3. A parabola which represents y' opens down with x-intercepts at x = -4 and x = 0. Sketch this parabola, and use it to sketch y and y''. 4. A non-lethal virus spreads through an enclosed space. The number of active cases of the virus, N, is a function of the percentage of people (as a percent, not the related decimal) who have received a vaccine shot, v. Meanwhile, the administrator of this enclosed space keeps track of the total cost of administering the vaccine shot, C, in dollars. The cost is also a function of the percentage of people who have received a vaccine shot. a) Describe what is meant by N'(70) = -23. b) Use function notation to model the following: 'The cost of the vaccine shot is 15 dollars when 1 percent of the people have been vaccinated.' c) An administrator in a separate enclosed space finds that N'(v) 0 for all domain of v. How should the administrator interpret this finding?