The profit function $($in millions$)$ for a beverage company for the years $2010$ through $2016$ can be approximated by $f(x)=-25x^2+750x-3391,$ where $x=10$ corresponds to the $y$ ear $2010.$

$($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 $f(x).$

$f^{\text{'}}(x)=$

A local maximum profit occurred in the year

$($b$)$ The maximum profit was $ $$ million.

$($Simplify your answer. Round to the nearest integer as needed.$)$