Let f:(a, b) → R be twice differentiable function such that f(x)=∫_a^x g(t) d t for a differentiable function g(x). If f(x)=0 has exactly five…

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