1. The figure below shows the graph of f', the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4. (6, 4) (20) (5, 0) (3, -1) (0, -2) (4, -2.5) (-2, -3) Find the x-coordinate of each of the points of inflection of the graph of f. Justify your answer. (10 points)2. A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the velocity of the car when t = 6? You must show your work and include units in your answer. (10 points)3. Show that f(x) = x3 and g(x) = 200x3 grow at the same rate. (10 points) B i U Font Family 4. A radar gun was used to record the speed of a runner (in meters per second) during selected times in the first 2 seconds of a race. Use a trapezoidal sum with 4 intervals to estimate the distance the runner covered during those 2 seconds. Give a 2 decimal place answer and include units. (10 points) t 0 0.5 1.2 1.5 2 v(t) 0 4.5 7.8 8.3 9.01+7 5. Water is poured into a bucket according to the rate F(t) = , and at the same time empties out through a hole in the bottom at the rate E(t) = !" , with both F(t) and E(t) measured in pints per minute. How much water, t+2 to the nearest pint, is in the bucket at time t = 5 minutes. You must show your setup but can use your calculator for all evaluations. (10 points)