Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $ \ne $ 0 for all x $ \in $ R. If $\left| {\matrix{ {f(x)} & {f'(x)} \cr {f'(x)} & {f''(x)} \cr } } \right|$ = 0, for all x$ \in $R, then the value of f(1) lies in the interval :