Let $f:(\mathrm{a}, \mathrm{b}) \rightarrow \mathrm{R}$ be twice differentiable function such that $\mathrm{f}(\mathrm{x})=\int_{\mathrm{a}}^{\mathrm{x}} \mathrm{g}(\mathrm{t}) \mathrm{dt}$ for a differentiable function $\mathrm{g}(\mathrm{x})$. If $f(x)=0$ has exactly five distinct roots in $(a, b)$, then $g(x) g^{\prime}(x)=0$ has at least :
