Determine the location of each local extremum of the function. f(x) = -x3+6x- - 9x + 1 What is/are the local minimum/minima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The local minimum/minima is/are at x = (Use a comma to separate answers as needed. Type integers or simplified fractions.) O B. The function has no local minimum.Use the rst derivative test to determine the location of each local extremum and the value of the function at this extremum. x)=2xe '5" Identify the location and function value of the maximum of the function, if any. Select the correct answer below and, if necessary, fill in any answer boxes within your choice. 0 A- The function has a local maximum of El atx= El. (Use a comma to separate answers as needed. Type exact answers in simplied form.) C) B. The function does not have a local maximum. The prot function [in millions} for a beverage company for the years 2010 through 2015 can be approximated by {(x] = 31){2 + 582): 192?, where 1:10 corresponds to the year 2D1U. [a] During what year did a local maximum prot occur? [b] What was the maximum prot? [a] A local extremum occurs at a critical number of f. Because the derivative exists for every x, the onlyr critical number(s} occur where the derivative is zero. Find the derivative of x}. f'ix} = E