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