AP Calculus Unit 5 Test 1. Find the equation of the line tangent to 3. Find the value of c that satisfies the MVTD for y =5x' - 20x +10 at x = 2. f(x) = x -6x +5 on the interval [3, 8]. (A) y-10 = 10(x-2) (A) 5 (B) y +10= 40(x+2) (B) 11 (C) y-10 = 40(x -2 2 (C) 11 (D) y-10= 90(x + 2) (D) There is no value of c. 2. Find the equation of the line normal to y = 4sec(2x) 4. Find the value of c that satisfies the MVTD for at x = 2 f(x ) =2 - on the interval [2, 6]. (A) y+4V2 =82 x- (A) -2 (B) 6 (B) y-4V2 = -8V2 x- (C) 8 (D) There is no value of c. (C) y+ 4V2 = 8 1 2 * + (D) y- 4V/2 = 8/2 8 5 A rectangle has its base on the x-axis and its two At what value(s) of x does the curve upper corners on the semicircle y = v200 - x2. y= x' -12x3 +120 have a point (or points) of Find the value of x that maximizes the area of the inflection? rectangle. (A) (4, -8) (A) 0 (B) (0, 120) (B) 5 (C) (8, -136) (D) (-4, -136) (C) 10 (D) V200 9 On what interval is the curve y = sinx + 3 cosx 6 An open rectangular box with a square base is to decreasing on [0, n]? have a volume of 108 in'. Find the dimensions of the box that minimize its surface area (base by height). (A) 0, (A) 3 in. by 6 in. (B) 6 in. by 6 in. (B) (C) 3 in. by 3 in. D) 6 in. by 3 in. . Find the coordinates of the maximum and minimum (if they exist) of y= x' -3x -24x+6. (D) The function is always increasing. Minimum Maximum (A) (-4, -10) (2, 46) (B) (4, -74) (-2, 34) (C) (1, -20) None (D) (1, -20) (2, 46) Source: Princeton Review AP Calculus Prep & AP Classroom Question BankAP Calculus Unit 5 Test A 25 ft ladder is sliding down a wall 2116st. How fast is the bottom of the ladder sliding out when the top of the ladder is 20 ft from the ground? (A) 2 fits (B) 6 Ms (C) 8 ts (D) 15 ms A baseball diamond has right angles at each of the bases. which are 90 fl apart. A baseball player is running from second base to third base at a rate of 30 f Us. How fast is the distance between the player and home plate changing when the player is halfway from second base to third base'? (A) ms : -l3.'HC ['le J3 (B) 30 fIJ'S (C) 339qu = #6035 \"F175 J5 (D) l35 {US I 2.. A spherical balloon is deating at 24i't' ins. How fast is the surface area of the balloon decreasing when the radius of the balloon is 6 in? (A) 6ain.=rs (B) 4331111.sz (C) -16rrin.'-ls (D) -24rrin.3t's Find where the velocity of a particle is zero if its position function is (x): = r\" 21'. where t > 0. (A) i=3? 1 B =__ ()td (C) i=1 (D) :35 If the position function of a particle is x(t')= 4r' 12:2 +18, r> 0, at what time is the panicie changing direction? {A} r=0 l B =_ (J I 2 (C) 1:1 (D) r=2 Source: Princeton Review AP Calculus Prep 8!. AP Classroom Question Bank AP Calculus Unit 5 Test 15. y = f(x) 0 The graph of y = f(x) is shown in the figure above. On which of the following intervals are - > 0 and dry 2 (B) x 4 only (E) x > 6 only Source: Princeton Review AP Calculus Prep & AP Classroom Question BankAP Calculus Unit 5 Test ( 7. For what values of x does the graph of y = 3a + 10x* have a point of inflection? (A) x = -3 only (B) x = -2 only (C) x = 0 only (D) x = 0 and x = - (E) x = 0 and x = -2 18, If f"(x) =x(x + 2) 2, then the graph of f is concave up for (A) x0 (C) -20 (E) all real numbers 19 Let g be the function defined by g(x) = [a| - 3|x + 1|. What is the absolute maximum value of g on the closed interval [-2, 2] ? * NOTE * (A) Ifexll'= fix f'(x) (B) -1 ( fox)1 (C) -3 (D) -7 you'll need this formula for # 19 20 . Let g be the function given by g(x) = 3x4 - 8x3. At what value of a on the closed interval [-2, 2] does g have an absolute maximum? (A) -2 (B) 0 (C) N (D) Source: Princeton Review AP Calculus Prep & AP Classroom Question Bank