Solve this following


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


  1. twelve roots in $(a, b)$

  2. five roots in $(a, b)$

  3. seven roots in $(a, b)$

  4. three roots in $(a, b)$

Correct Option: , 3


$f(x)=\int_{a}^{x} g(t) d t$

$f(x) \rightarrow 5$

$f^{\prime}(x) \rightarrow 4$

$g(x) \rightarrow 4$

$g^{\prime}(x) \rightarrow 3$


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