Page 1 of 3 ZOOM Provide an appropriate response. 1 ) A 26-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 2 feet per second, at what rate is the bottom of the ladder moving away from the wall when the bottom of the ladder is 10 feet away from the wall? A) 4.8 ft/sec B) 9.6 ft/sec C) 5.2 ft/sec D 2.4 ft/sec 2) Use the first derivative test to determine the local extrema, if any, for the function: f(x) =3x4 - 6x2 +7. A) local max at x = 0 and local min at x =-1 and x = 1 Reuther cap B) local max at x = -1 and local min at x = 0 and x = 1 PROUDLY SOURCED IN CALIFORNIA. S COUNTY LOSS DOMIT PRESS C) local min at x = 0 and local max atx = -1 and x = 1 ASTIC D local max at x = 1 and local min at x = 0 UTLE WTHEADWATER. COM ING: Cap is a small part and poses a GA GRY 3) Find the inflection point(s) for f(x) =x3 - 6x - 1. NG HAZARD, particularly for children. A) (0, -6) B) (0, -1) C) (-1, 6) D (1, -1) 4) Find the critical values and determine the intervals where f(x) is increasing and the intervals where f(x) is decreasing for the function f(x) =x3 + 3x2 - 24x + 6. A) decreasing on (709, -4) and (2, co); increasing on (-4, 2) B) increasing on (, -4) and (2, w.); decreasing on (-4, 2) @) increasing on (w, -4); decreasing on (-4, 2) D increasing on (ro, -4) and (2, w); decreasing on (-4, ") 5) Assume x - x(t) and y = y(t). Find @x if x2 + y2 = 25 and -dy = 3 when x = 3 and y = 4. A ) 4 B) - 6 C) 6 D - 4 6 ) Find the absolute maximum and minimum values of f(x) =9x3 - 54x2 + 81x + 13 on the interval [-6, 2]. A ) max f(x) = f(1) = 4361 B) max f(x) = f(1) = 4361 min f(x) =f(-6) = -49 min f(x) = f(-6) = 49 C) max f(x) = f(1) = 49 D max f(x) = f(-6) =-4361 min f(x) = f(1) = 49 min f(x) =f(-6) = -4361 7 ) Find f"(x) for f(x) =5x4 - 6x2+7. B ) f' ( x ) = 60 *2 - 12 C ) f ( x ) = 20x2 - 12x Df' ( x ) = 60x2 - 12x A) f (x) = 20x2- 12 5:00 PM 16 5/1/20238) Find dy/dx by implicit differentiation. 2xy - y2 = 1 A ) dy x - y B) dy dx x - y C) dx y-x D dy dx y - x 9) Determine the interval(s) over which f(x) =(x+3) is concave upward. A) (-00, 00) B) (-0, 3) C) (-3, 00) D (-0, -3) Solve the problem. 10) The annual revenue and cost functions for a manufacturer of zip drives are approximately R(x) =520x - 0.02x2 and C(x) = 160x + 100,000, where x denotes the number of drives made. What is the maximum annual profit? A) $1,520,000 B) $1,620,000 C) $1,720,000 D $1,820,000 Find the limit, if it exists. 11 ) Find lim In x x - out X A) - BO C) D 1 Find the intervals where f"(x) 0 as indicated. 12) f'(x) 0 as indicated. 12) f'(x) 0. 14) soofy 400- 300- 200+ 100+ -2 -Zoo -300- -400- soot A) f (x) > 0 on [-36, 36], f'(x) 0 on (-0, -6] ~ [6, ~), f(x) 0 on (=0, 6], f(x) 0 on [-6, 6], f(x) , -6] ~ [6, ) 5:01 PM 5/1/2023