A continuous and differentiable function $y = f\left(x\right)$ is such that its graph cuts the line  $y = px + q$ at $m$ distinct points. Minimum number of points at which $\mathrm{f} \text{'}\text{'}\left(\mathrm{x}\right)=0$ is /are

Very obviously if line cuts the graph at m points then using LMVT $\exists$ at least (m – 1) points where f¹(x) = p (slope of line)

$\therefore$ using Rolle’s $\exists$ at least (m – 2) points where f¹¹(x) = 0