Let \( f:(a,b)\to \mathbb{R} \) be twice differentiable function such that \( f(x)=\int\limits_{a}^{x} g(t)\,dt \) for a differentiable function \( g(x) \). If \( f(x)=0 \) has exactly five distinct roots in \( (a,b) \) then \( g(x)\,g'(x)=0 \) has at least:
