2. [0/1 Points] DETAILS l PRE' MY NOTES ASK YOUR TEACHER Find the derivative of the function. f(t) = 4(t4 2)5 W) = 80:3[z42]5 x 12. [0/1 Points] DETAILS PREVIOUS ANSWERS 1 MY NOTES ASK YOUR TEACHER | PRACTICE ANOTHER Find the derivative of the function. 9(5) = (55 + if\" S 3. [1/2 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANO Find the first and second derivatives of the function. f ( x) = x(x2 + 6)2 f'( x ) = ( x 2 + 6) (2x2 + 6, X f"(x) = 20x3 + 72x6. [0/1 Points] DETAILS l PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER | PRACTICE AND Find the third derivative of the given function. f(x) = 12 flfl(x) = 8. [-/1 Points] DETAILS TANAPCALCBR10 3.6.040. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Distance Between Two Cars A car leaves an intersection traveling west. Its position 4 sec later is 18 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 4 sec later is 27 ft from the intersection. If the speeds of the cars at that instant of time are 8 ft/sec and 12 ft/sec, respectively, find the rate at which the distance between the two cars is changing. (Round your answer to one decimal place.) ft/s Need Help? Read It Watch It Talk to a Tutor 9. [-/1 Points] DETAILS TANAPCALCBR10 3.6.044. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Effect of Price on Supply of Eggs Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. 625p2 - x2 =100 If 30000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 4c/carton/week, at what rate is the supply changing? (Round your answer to the nearest whole number. ) (Hint: To find the value of p when x = 30, solve the supply equation for p when x = 30.) cartons per week Need Help? Read It Watch It Talk to a Tutor 10. [-/1 Points] DETAILS TANAPCALCBR10 3.6.050. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 6 in. long and increasing at the rate of 0.3 in./s. How fast is the volume of the cube changing (in cu in/s) at that instant of time? cu in/sDistance Between Two Ships Two ships leave the same port at noon. Ship A sails north at 12 mph, and ship B sails east at 11 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.) mph Need Help? l Submit Answer Docking a Boat A boat is pulled toward a dock by means of a rope wound on a drum that is located 5 ft above the bow of the boat. If the rope is being pulled in at the rate of 5 ft/s, how fast (in ft/s) is the boat approaching the dock when it is 33 ft from the dock? (Round your answer to one decimal place.)