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1 y 3 5 Graph of f ' x 76. The graph of f ', the derivative f, is shown above for x 5. n what intervals is f increasing? (A) [, ] only (B) [, 3] (C) [3, 5] only (D) [0,.5] and [3, 5] (E) [, ], [, ], and [, 5]

2 y 3 x Graph of f 77. The figure above shows the graph of a function f with domain 0 x. Which of the following statements are true? I. lim f ( x) x II. lim f ( x) + x exists. exists. III. lim f ( x) x exists. (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III The first derivative of the function f is defined by f '( x) sin( x x) what interval(s) is f increasing? (A) x.5 (B) x.69 (C).5 x.875 (D) x.5 and.875 x (E) 0 x and.69 x = for 0 x. n

3 5 79. If f ( x) dx= 7 and f ( x) dx=, 5 what is the value of ( ) 5 5 (A) (B) 3 (C) 0 (D) 3 (E) f x dx? 80. The derivative of the function f is given by f ( x) x ( x ) inflection does the graph of f have on the open interval (, )? ' = cos. How many points of (A) ne (B) Two (C) Three (D) Four (E) Five

4 8. If G( x ) is an antiderivative for f ( x ) and G ( ) = 7, then ( ) (A) f ' ( ) (B) 7 + f '( ) (C) f () t dt ( ) (D) 7 + f () t dt (E) 7 f () t dt + G = 8. A particle moves along a straight line with velocity given by vt () 7 (.0) t t 0. What is the acceleration of the particle at time t = 3? (A) 0.9 (B) (C) 5.86 (D) (E) = at time

5 83. What is the area enclosed by the curves = and y = x+ 5? 3 y x x x (A) (B).833 (C).583 (D).333 (E) 3 y x Graph of f ' 8. The graph of the derivative of a function f is shown in the figure above. The graph has horizontal tangent lines at x =, x =, and x = 3. At which of the following values of x does f have a relative maximum? (A) only (B) only (C) only (D) and 3 only (E),, and

6 x 3 f ( x) f '( x) The table above gives values of a function f and its derivative at selected values of x. If is continuous on the interval [, ], what is the value of f ( ) ' x dx? (A).5 (B).5 (C) 0 (D).5 (E).5 f '

7 t 0 3 vt () The table gives selected values of the velocity, vt (), of a particle moving along the x-axis. At time t = 0, the particle is at the origin. Which of the following could be the graph of the position, x(), t of the particle for 0 t? (A) x () t (B) x () t t t (C) x () t (D) x () t t t (E) x () t t

8 87. An object traveling in a straight line has position x() t at time t. If the initial position is ( 0) 3 x = and the velocity of the object is vt () = + t, what is the position of the object at time t = 3? (A) 0.3 (B).5 (C).5 (D) 6.5 (E) The radius of a sphere is decreasing at a rate of centimeters per second. At the instant when the radius of the sphere is 3 centimeters, what is the rate of change, in square centimeters per second, of the surface area of the sphere? (The surface area S of a sphere with radius r is S = π r ) (A) 08π (B) 7π (C) 8π (D) π (E) 6π

9 89. The function f is continuous for x and f ( ) f ( ) = = 0. If there is no c, where < c <, for which f '( c ) = 0, which of the following statements must be true? (A) For k, < < ( ) (B) For k, f ' k > 0. < < ( ) (C) For k, f ' k < 0. < < f '( ) (D) For k, < < '( ) k exists. (E) For some k, where k, f k exists, but f ' is not continuous. < < f '( ) k does not exist. 90. The function f is continuous on the closed interval [, ] and twice differentiable on the open interval (, ). If f '3 ( ) = and ( ) following could be a table of values for f? (A) (B) (C) f " x < 0 on the open interval (,), which of the x f ( x) x f ( x) x f ( x) (D) (E) x f ( x) x f ( x)

10 cos x 9. What is the average value of y = x + x + on the closed interval [, 3]? (A) (B) (C) 0.83 (D) 0. (E) 0.73 miles River City 7 miles 9. A city located beside a river has a rectangular boundary as shown in the figure above. The population density of the city at any point along a strip x miles from the river s edge is f ( x ) persons per square mile. Which of the following expressions gives the population of the city? (A) f 0 ( x ) dx (B) ( ) 7 f x dx 0 (C) ( ) 8 f x dx 7 (D) f 0 ( x ) dx 0 7 (E) ( ) f x dx 0