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Consider the position function s(t) = 16t2 + 96t representing the position of an object moving vertically along a line. Sketch a graph of s with the secant line passing through (0.5,s(0.5)) and (25(2)). Determine the slope of the secant line and explain its relationship to the moving object. Sketch the graph of s with the secant line. Choose the correct graph below. {:2 A. 11:} B. 1:} C. S Q S Q S Q 128 Q 128 Q 128 Q El ['1' El 44 44 44 t t t 0.5 2 015 2 0'5 2 The slope of the secant line is msec =D. (Type an integer or a decimal.) What is the relationship of the slope to the moving object? if) A. The slope is the maximum velocity of the object. ("II B. The slope is the average velocity of the object over the interval [44,128]. {if} C. The slope is the average velocity of the object over the interval [05,2]. Cir D. The slope is the instantaneous velocity when t= 2. Use the graph to evaluate the limit. OA. O lim f(x) O B. does not exist X- 0 + OC. -2 O D. 2 3- 2 - -2 - 1 1 2 -3- -4-Explain the meaning of Iim f(X) = L. X>a Choose the correct answer below. 1:! A. As X approches a from either side, the value of f(X) approaches L. 1:] B. As X approaches a from the left, the value of f(X) approaches L. 1:} C. As X approaches a from the right, the value of f(X) approaches L. Determine whether the following function is continuous at a. Use the continuity checklist to justify your answer. x2 64 KM: X-8 6 ifx=8 ifx8 ;a=8 Select all that apply. A. The function is continuous at a = 8. B. The function is not continuous at a = 8 because f(8) is undefined. C. The function is not continuous at a = 8 because lim f(x) does not exist. x>8 D. The function is not continuous at a = 8 because lim f(x) f(8). x>8 Use the following information to graph the function fover the closed interval [ 5,6]. i) The graph of f is made of closed line segments joined end to end. ii) The graph starts at the point ( 5,1). iii) The derivative of f is the step function in the figure shown here. A v Use the graph offto sketch a graph of f'. Choose the graph of f'. IV A \"I II ,.II II a. In "l'l ml- nun. If f is a one-to-one function with f(5) = 9 and f'(5) = 8, what is the value of (F1) /(9)? E> (F1) [(9): D (Simplify your answer.) Solve the problem. Round your answer, if appropriate. One airplane is approaching an airport from the north at 211 km/hr. A second airplane approaches from the east at 167 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 36 km away from the airport and the westbound plane is 17 km from the airport. Cl A. - 131 km/hr (:i B. - 393 km/hr (:3 C. - 262 km/hr (:3 D. - 524 km/hr Determine from the graph whether the function has any absolute extreme values on the interval [a, b]. O A. Absolute minimum only O B. No absolute extrema O C. Absolute minimum and absolute maximum O D. Absolute maximum only a