Question 1 (Essay Worth 10 points) (08.01) The gure 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. (-2. -3) Find the x-value where fattains its absolute minimum value on the closed interval from x = 2 to x = 6. Justify your answer. Question 2 (Essay Worth 10 points) is (08.01) A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 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. Question 3 (Essay Worth 10 points) (08.02) Show that f(x) = x3 and g(x) = 200x3 grow at the same rate. Question 4 (Essay Worth 10 points) (08.03) in: A radar gun was used to record the speed of a swimmer (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 swimmer covered during those 2 seconds. Give a 2 decimal place answer and include units. t 0 0.4 1.0 1.5 2 v(t) 0 4 7.2 8.6 9.0 Question 5 (Essay Worth 10 points) (08.04) 2 Oil ows into a tank according to the rate F(t): % and at the same time empties out at the rate E(t) = the tank at time t = 12 minutes. You must show your setup but can use your calculator for all evaluations |n(l+7) 1+2 [E3 , with both F(t) and E(t) measured in gallons per minute. How much oil, to the nearest gallon, is in