Answer Happy

36. Given a function f, a critical point e in the domain of f only occurs when f'(c) = 0. a. True b. False 37. The length of a rectangle is increasing at the rate of 2 meters per second, while the width is increasing at the rate of 1 meter per second. When the length is 5 meters and the width is 3 meters, how fast is the area increasing? a. 5 m²/s b. 11 m²/s c. 6 m²/s d. 10 m²/s e. None of the above 38. A ladder 10 meters long is leaning against a wall, with the foot of the ladder 8 meters away from the wall. If the foot of the ladder is being pulled away from the wall at 3 meters per second, how fast is the top of the ladder sliding down the wall? a. 5 m/s b. 8 m/s c. 2 m/s d. 4 m/s e. None of the above 39. A small boy standing in a flat field watches a balloon rise in the distance. The balloon leaves the ground 500 m away from the boy and rises vertically at the rate of 7 m/minute. At what rate is the angle of inclination of the boy's line of sight (0 in radians) increasing at the instant when the balloon is exactly 500 m above the ground? a) s radians/minute b) ooo radians/minute 1000 c) radians/minute d) radians/minute 14 250 e) None of the above. BOY 40. Which of the following is the statement of the Mean Value Theorem? a. Assume that is continuous on the closed interval [a, b] and either f(a) < a < f(b) or f(a) > a> f(b). Then there exists a <e<b such that f(c) = a. 。) MILL b. Assume that f is continuous on (a, b) and f is differentiable on (a, b). Then there exists a < c < b such that f'(c) 10-10) 6-a P 500 m c. Assume that is continuous on (a, b) and f is differentiable of (a, b) and that f(a) = f(b) = 0. Then there exists a<c<b such that f'(c) = -1)=0. d. None of the above