Application Of Derivatives

Let \(A = [{a_{ij}}]\) be a 3 \(\times\) 3 matrix, where \({a_{ij}} = \left\{ {\matrix{ 1 & , & {if\,i = j} \cr { - x} & , & {if\,\left| {i - j} \right| = 1} \cr {2x + 1} & , & {otherwise.} \cr } } \right.\)

Let a function f : R \(\to\) R be defined as f(x) = det(A). Then the sum of maximum and minimum values of f on R is equal to: