Let \( \mathrm{f} \) be a twice differentiable function defined on \( R \) such that \( f(0)=1, f^{\prime}(0)=2 \) and \…

Let \( \mathrm{f} \) be a twice differentiable function defined on \( R \)

such that \( f(0)=1, f^{\prime}(0)=2 \) and \( f^{\prime}(\mathrm{x}) \neq 0 \) 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

[JEE Main 2021, 24 Feb (Shift 2)]