d. e do .860an u dx . none of these a. {00, no) a .True b. False Unit 2 Evaluation 20. Where is x) = )1 3x differentiable? 22. Find the equation of the line tangent to x) = 181 3 x4 19. If you combine the chain rule with the tangent rule, d1 [tan u] = x atx= -2. 23. The derivative of the sum of two functions is the sum of their derivatives. MTHH 071 24. The derivative of the difference of two functions is the difference of their derivatives. a. True b. False 25. An object moves according to the position equation s(t) = t + sin t, where s is measured in meters. What is the average velocity of the object during the time interval from t = 0 to t = 27 seconds? a. 0.318 m/s b. 1 m/s c. 2 m/s d. 3. 14 m/s e. none of these 26. An object moves according to the position equation s(t) = t + sin t, where s is measured in meters. What is the average acceleration of the object during the time interval from t = 0 to t = 2 7 seconds? a. 0 m/s b. 1 m/s2 c. 2 m/s d. 3.14 m/s e. none of these 27. An object moves according to the position equation s(t) = sin t, where s is measured in meters. What is the instantaneous velocity of the object at time t = 2 7 seconds? a. 0 m/s b. 1 m/s c. 2 m/s d. 3.14 m/s e. none of these 28. An object moves according to the position equation s(t) = sin t, where s is measured in meters. What is the instantaneous acceleration of the object at time t = 2 x seconds? a. 0 m/s2 b. 1 m/s2 c. 2 m/s2 d. 3.14 m/s e. none of these Unit 2 Evaluation 182 MTHH 07129. You can buy rectangular-shaped sponges that have been vacuum packed to take up less volume for shipment and storage. When they are soaked in water, the volume expands in such a way that the linear dimensions of the soaked sponges all increase by the same ratio. A particular sponge starts out with dimensions of 1 inch high, 4 inches wide, and 6 inches long. When the sponge is put in water, at the end of the rst hour its height has doubled and is increasing at the linear rate of 1 inch per hour. So, at the end of the first hour a. the volume of the sponge is 48 cubic inches, and its volume is increasing at the rate of 3 cubic inches per hour. b. the volume of the sponge is 48 cubic inches. and its volume is increasing at the rate of 9 cubic inches per hour. 0. the volume of the sponge is 48 cubic inches. and its volume is increasing at the rate of 27 cubic inches per hour. d. the volume of the sponge is 192 cubic inches, and its volume is increasing at the rate of 288 cubic inches per hour. 30. A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cmalhr. At what rate is its diameter decreasing? a. cm/hr 31. A water heater in the shape of a circular cylinder is standing vertically. resting on one of the round ends. The tank is 60 inches tall and has a volume of 30 gallons. If water is flowing into the tank at the rate of 5 gallons per minute, at what rate is the level of the water in the tank increasing? a. 10 inches per minute b. 12 inches per minute c. 15 inches per minute d. 20 inches per minute Unit 2 Evaluation 183 MTHH 071 32. A 40 foot long ladder is resting against a wall. The base of the ladder at point B is being pulled away from the wall at the rate of 1 foot per second. If the ladder remains in contact with the ground and with the wall as the base of the ladder is pulled away from the wall, how fast is the top of the ladder (point A) moving down the wall at same the time that the bottom of the ladder (point B) is 39 feet from the base of the wall? a. 1 ft/sec b. 2.2 ft/sec c. 4.4 ft/sec d. 8.8 ft/sec e. 10.4 ft/sec 33. Use the alternative form of the derivative to find the derivative of the function f(x) = x - 9 at x = 5. a. f '(5) = 1 b. f '(5) = 250 c. f '(5) = 2 d. f '(5) = 125 e. f '(5) = 10 34. Describe the x-values at which f(x) = x2 - is differentiable. - 9 a. f(x) is differentiable at x = 13. b. f(x) is differentiable everywhere except at x = 13. c. f(x) is differentiable everywhere except at x = 0. d. f(x) is differentiable on the interval (-2, 2). e. f(x) is differentiable on the interval (2, co). 35. Describe all values of x, if any, at which the graph of the function has a horizontal tangent. y(x) = x + 12x- + 8. a. x = 0 b. x = -8 c. x = 0 and x = -8 d. x = 0 and x = 8 e. The graph has no horizontal tangents. Unit 2 Evaluation 184 MTHH 071