13. 14. 15. 16. 17. (1y Find : ifX2y+ y2 = X. F' d 'f = t + 1n : I an . X (X y) A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 12811 cubic inches. At what rate is the length ii changing when the radius r is 2.5 inches? [Hint: V: anh] Find : y? = 6x2 The cost of producing xunits ofa product is C=90x + 225i}. For one week, management determined the number of units produced at the end of 1\" hours during an 8-hour shift. The average values ofxfor the week are shown in the table. t 1 2 3 4 5 6 7 8 X 18 62 135 214 276 340 388 399 a) Use a graphing utility to find a cubic model for the data. b) Use the Chain Rule to find dC/a't. c) Find the rate of change ofthe (lost at 5 hours. 10. 11. 12. 13. 14. 15. 16. 17. Find f'(X) if f(X) = 55in2 (4x2-5x+1) A balloon rises at the rate of 8 feet per second from a point on the ground 60 feet from an observer. Find the rate of change ofthe angle of elevation when the balloon is 25 feet above the ground. A 5-meter-long ladder is leaning against the side ofa house. The foot ofthe ladder is pulled away from the house at a rate of 0.4- m/sec. Determine how fast the top ofthe ladder is descending when the foot of the ladder is 3 meters from the house. I ' I 2 2 Find . lfxy+y _X. F'nd TX: tan x+ 1 . 1 ( y). A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 12811 Cubic inches. At what rate is the length i: changing when the radius r is 2.5 inches? [Hint: V: ann] [12 Find y : y? = 6x2 dxz The cost of producing Xunits ofa product is C=90x + 2250. For one week, management determined the number of units produced at the end of 1\" hours during an 8-hour shift. The