JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 23

Let $f:[0,1]\to\mathbf R$ be a twice differentiable function in (0, 1) such that $f(0)=3$ and $f(1)=5$. If the line $y=2x+3$ 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 $f''(x)=0$, is ______.