Let $f$ be a twice differentiable function defined on $R$ such that $f(0)=1, f^{\prime}(0)=2$ and $f^{\prime}(x) \neq 0$ for all $x \in R$. If $\left|\begin{array}{ll}f(x) & f^{\prime}(x) \\ f^{\prime}(x) & f^{\prime \prime}(x)\end{array}\right|=0$, for all $x \in R$, then the value of $f(1)$ lies in the interval:
