Let \(f\) be a twice differentiable function defined on \(R\) such that \(f(0) = 1,\ f '(0) = 2\) and \(f'(x) ≠ 0\) for all \(x ∈ R\). If \(\left| {\begin{array}{*{20}{c}} {{\rm{f}}\left( {\rm{x}} \right)}&{{\rm{f'}}\left( {\rm{x}} \right)}\\ {{\rm{f'}}\left( {\rm{x}} \right)}&{{\rm{f''}}\left( {\rm{x}} \right)} \end{array}} \right|=0\), for all \(x ∈ R\), then the value of \(f(1)\) lies in the interval:
1
(0, 3)
2
(3, 6)
3
(6, 9)
4
(9, 12)