Mathematics - Application of Derivative Question with Solution | TestHub

$\because f(b)f(c)<0$ and $f(c)f(d)<0$

$\Rightarrow \mathrm{f}(\mathrm{x})=0$ has at least four roots,

$\mathrm{a},{\mathrm{c}}_1,{\mathrm{c}}_2,\mathrm{e}$, Where ${\mathrm{c}}_1\in (\mathrm{b},\mathrm{c})$ and ${\mathrm{c}}_2\in (\mathrm{c},\mathrm{d})$. Then, by RT, ${\mathrm{f}}^1(\mathrm{x})=0$ has

at least three roots in, $\left(a,c_1\right),\left(c_1,c_2\right),\left(c_2,e\right)$

$\therefore \mathrm{f}(\mathrm{x}){\mathrm{f}}^1(\mathrm{x})=0$ has at least 7 roots, by RT and hence,

$g(x)=\frac{d}{dx}\left\{f(x)f^1(x)\right\}=0$ has at least 6 roots