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A person coughs when a foreign object is in the windpipe. The velocity of the cough depends on the size of the object. Suppose a person has a windpipe with a 22-mm radius. If a foreign object has a radius r, in millimeters, then the velocity V, in millimeters/second, needed to remove the object by a cough is given by the following equation, where k is some positive constant. For what size object is the maximum velocity needed to remove the object? V(r) = k (2212 - 3), Osis 22 An object that has a radius of will need maximum velocity to remove it. (Type an integer or a simplified fra mm mm/second mmGraph the following function. Then estimate any relative extrema. f(x) = x(2-3x)3 Choose the correct graph below. All windows are displayed [ - 1,1,0.2] by [ - 1, 1,0.2]. O A. O B. O C. O D. What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Type an ordered pair. Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) O A. There are two relative extrema. In order of increasing x-value, the coordinates of the relative extrema are and. B. There are three relative extrema. In order of increasing x-value, the coordinates of the relative extrema are , , and O C. There is one relative extremum. The coordinate of the relative extremum is O D. There are no relative extrema.An employee's monthly productivity M, in number of units produced, is found to be a function of the number t of years of service. For a certain product, a productivity function is shown below. Find the maximum productivity and the year in which it is achieved. M(t) = - 212 + 96t + 140, Osts 40 The maximum productivity is achieved in year. The maximum productivity is units