The profit function (in millions) for a beverage company for the years 2008 through 2016 can be approximated by f(x) = - 26x + 728x-2643, where x= 8 corresponds to the year 2008. | (a) During what...

Extracted text: The profit function (in millions) for a beverage company for the years 2008 through 2016 can be approximated by f(x) = - 26x + 728x-2643, where x= 8 corresponds to the year 2008. | (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) =| %3D A local maximum profit occurred in the year| million. (b) The maximum profit was $ (Simplify your answer. Round to the nearest integer as needed.)