Let f:[0,1] → 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…

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