For Exercises 1-4, use the graphs of fand g to describe the motion of a particle whose position at time t is given by x = f(t), y = g(t).X 2 f (t) 2 g (t) 1 2 3 4 1 2 3 4 2. 8. A circle of radius 2 centered at the origin traced clockwise starting from (2,0) when t = 0. Exercises 12-17 give parameterizations of the unit circle or a part of it. Describe in words how the circle is traced out, including when and where the particle is moving clockwise and when and where the particle is moving counterclockwise. 12. x = sint, y = cos tIn Exercises 21-26, the parametric equations describe the motion of a particle. Find an equation of the curve along which the particle moves. For Exercises 31-34, find the speed for the given motion of a particle. Find any times when the particle comes to a stop.34. x =12 At, y = to - 12t50. For x and y in meters, the motion of a particle is given by x =t' - 3t, y =t2 - 2t, where the y-axis is vertical and the x-axis is horizontal. a. Does the particle ever come to a stop? If so, when and where? b. Is the particle ever moving straight up or down? If so, when and where? c. Is the particle ever moving straight horizontally right or left? If so, when and where?1. {10 pts total} The equation 2x3 y'1 + x2y3 = 19 defines a curve in the plane that includes the point (x. y) = (2.1). Show your work for ALL ports below. a. {5 pts) Use implicit differentiation to find the slope of this curve at the point {x,y) = (2,1). b. [3 pts) Use your answer from part (a) to find an equation for the tangent line to the curve at the point (2,1). :2. [2 pts) Use your answer from part {b} to estimate the v-coordinate of a point on this curve where x = 2.2. 2. (10 pts total) Let f be a function on the closed interval -3 s x 4 with f(0) = 3 and f(-1) = 2. The graph of f', the derivative of f, consists of a line segment and a semi-circle, as shown to the right. a. (2 pts) On what interval(s), if any, is f increasing? Explain how you know. Careful here - remember the graph shown at the right is the graph of f'. This is NOT the graph of f. graph of f' b. (2 pts) For what x-value does f have a relative minimum? Explain how you know. c. (2 pts) On what interval(s), if any, is f concave down? Explain how you know. d. (2 pts) Find the x-coordinate of each point of inflection of the graph of f on the open interval -3