K Consider xe y =4. (a) Find - by first solving the given equation explicitly for y in terms of x and then differentiating y. dx (b) Find - by implicit differentiation. (a) Solve the given equation explicitly for y in terms of x. y =(Type an exact answer.) (b) Which of the following shows the result of implicitly differentiating the given equation? OA. X- -ey =0 OB. xe y y +ey = 4 + ey = 4 OC. X-+ dx dx dx OD. X- day _ ey =4 O E. eyy+xey =0 OF. xe y y - ey =4 dx dx dx OG. xe y y + ey =0 OH. xe y y - ey =0 OI. X- dy + ey =0 dx dx dx Using either method, dx =. (Type an exact answer.)Given that x and y are functions of time, find the indicated rate of change. K dx Find when y = 3 and dy = 1, given that x = 9y - 216. dt dt dx (Round to two decimal places as needed.) dtK The profit function (in millions) for a beverage company for the years 2009 through 2017 can be approximated by f(x) = -29x-+ 870x - 3517, where x = 9 corresponds to the year 2009. (a) During what year did a local maximum profit occur? (b) What was the maximum profit? (a) A local extremum occurs at a critical number of f. Because the derivative exists for every x, the only critical number(s) occur where the derivative is zero. Find the derivative of f(x). f' (x) =_ A local maximum profit occurred in the year (b) The maximum profit was $ million. (Simplify your answer. Round to the nearest integer as needed.)