Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

Let $f:[0,1] \rightarrow \mathbf{R}$ be a twice differentiable function in $(0,1)$ such that $f(0)=3$ and $f(1)=5$. If the line $y=2 x+3$ intersects the graph of $f$ at only two distinct points in $(0,1)$, then the least number of points $x \in(0,1)$, at which $f^{\prime \prime}(x)=0$, is ____________.