1. [0/2 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 2.6.013. MY The radius r of a sphere is increasing at a rate of 3 centimeters per minute. (a) Find the rate of change of the volume when / = 9 centimeters. cm/min X (b) Find the rate of change of the volume when r = 34 centimeters. 204n cm/min X eBookAnalyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = 6x4 + 8x3 intercept (x, y ) = (0.0 ) u ( CO/ (smaller x-value) X (x, y ) = (0,0) (larger x-value) X relative minimum (x, y ) = (-1, -2) X relative maximum (x, y) = DNE points of inflection (x, y) = (smaller x-value) X (x, V) = (0,0) (larger x-value) X Find the equations of the asymptotes. (Enter your answers as a comma-separated list of equations.) DNE Use a graphing utility to verify your results. 2-1 214. [-/2 Points] DETAILS LARCALC11M 3.7.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must contain 405,000 square meters in order to provide enough grass for the herd. No fencing is needed along the river. What dimensions will require the least amount of fencing? X m y m x Need Help? Watch It eBook11. [3/5 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 3.3.035. MY NOTES ASK YOUR TEACHER PRACT Consider the following function. f(x) = 7x+ . (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) X = (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE. increasing (- 20, - #7 ) U ( $7:00 ) decreasing (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) 1 relative maximum (x, y) = V ,2V7 X relative minimum (x, y) = 2V7 X4. [0/2 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 2.6.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.30 meter per second. How fast is the end of the plank sliding along the ground when it is 1.6 meters from the wall of the building? (Round your answer to two decimal places.) 5 m 0.08 * m/sec Need Help? Watch It eBook13. [2/3 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 3.4.019. Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.) f(x) = 8 - 7x4 (x, V ) = 0.8 X Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave upward DNE concave downward (-00,0) U (0,00)15. [-I2 Points] LARCALCHM 3.7.038. MY NOTES ASK YOUR TEACHER Two factories are located at the coordinatea (7x, (I) and (x, D], and their power supply is at (D, h), as shown in the gure. Find y such that the total length of power line from the power supply to the factories is a minimum. y: 3. [012 Polnts] DETAILS PREVIOUS ANSWERS LARCALC11M 2.6.020. MY NOTES ASK YOUR TEACHER l PRACTIC A trough is 12 meters long and 3 meters across the top (see gure). Its ends are isosceles triangles with altitudes of 3 meters. (a) If water ls being pumped into the trough at 2 cubic meters per mlnute, how fast is the water levei rising when h is 1.5 meters deep? x mm (b) If the water is rlsing at a rate of 2.5 centimeters per minute when h = 2.5, determine the rate at which water is being pumped into the trough. _x mm 10. [-/2 Points] DETAILS LARCALC11M 3.9.041. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The range R of a projectile is shown below, where vo is the initial velocity in meters per second and 0 is the angle of elevation. R = . Vo (sin 20) 9.8 Use differentials to approximate the change in the range when Vo = 700 meters per second and @ is changed from 100 to 150. (Round your answer to the nearest whole number.) m eBook11. [-/2 Points] DETAILS LARCALC11M 3.7.025. MY NOTES ASK YOUR TEACHER PRACTICE AN A rectangle is bounded by the x-axis and the semicircle y = \\ 25 - x2 (see figure). What length and width should the rectangle have so that its area is a maximum? (smaller value) (larger value) 14 12 10 8 y 6 y = qr1(25 - x*2) 4 2 -10 8 6 -4 20 2 8 10 -2 Need Help? Watch It eBook6. [-/2 Points] DETAILS LARCALC11M 3.9.013. MY NOT Use the information to find and compare Ay and dy. (Round your answers to three decimal places.) y = 0.9x x = 1 Ax = dx = 0.1 Ay = dy = Need Help? Watch It eBook Submit Answer 7. [-/2 Points] DETAILS LARCALC11M 3.9.020. MY NOT Find the differential dy of the given function. (Use "dx" for dx.) y = 6x2/3 dy = Need Help? Watch It eBook12. [-12 Points] DETAILS LARCALCHM 3.7.029. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 34 centimeters (see figure). Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.) 13. [42 Points] AILS LARCALC11M 3.7.007. ASK YOUR TEACHER PRACTICE ANOTHER Find two positive numbers satisfying the given requirements. The product is 192 and the sum of the rst plus three times the second is a minimum. |:I (rst number) :I (second number) Need Help? .-w...- - ._ .\\ 14. [2/3 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 3.4.023. MY NOTES ASK YOU Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.) f(x) = xVx+ 12 ( x, V ) = DNE Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave upward -12,00 concave downward DNE eBook Viewing Saved Work Revert to Last Response5. [0.52 Points] ASKYOUR TEACHER PRACTICE ANOTHER PREVIOUS ANSWERS LARCALU 1 M 2.6.024. A boat is pulled into a dock by means of a winch 2 meters above the deck of the boat. (a) The winch pulls in rope at a late of 1.2 meters per second. Determine the speed of the boat when there is 5.6 meters of rope out. (Round your answer to two decimal places.) x W... What happens to the speed of the boat as it gets closer to the dock? The speed of the boat ' as it approaches the dock. {b} Suppose the boat is moving at a constant rate of 1.2 meters per second. Determine the speed at which the winch pulls in rope when there is a total of 5.6 meters of rope out. (Round your answer to two decimal places.) E x W... What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock? The speed at which the winch pulls in rope approad'ies -4 misec V x B. [-i'2 Points} LARCALCHM 3.9.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHI Find the differential 5')! of the glven function. (Use 'dx' for dx.) x + 2 9. [-12 Points] LARCALCHM 3.9.039. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTHI The period of a pendulum is given by the equation shown below, where l. is the length of the pendulum in meters, 9 is the acceleration due to gravity, and Tis the time in seconds. I\". T=2N 9 The pendulum has been subjected to an increase in temperature such that the length has increased by %% (a) Find the approximate percent change in the period. |:| % (b) Using the result in part (a), nd Hie approximaha error in this pendulum dock in 1 day. |:l min