Mathematics - Application of Derivative Question with Solution | TestHub

Let $f^{\prime }(x)=a{x}^2+bx+c\Rightarrow f(x)=\frac{a{x}^3}{3}+\frac{b{x}^2}{2}+cx+d$ $\Rightarrow f(x)=\frac{1}{6}\left(2a{x}^3+3b{x}^2+6cx+6d\right)$, Now $f(1)=f(0)=d$, then according to Rolle's theorem $\Rightarrow f^{\prime }(x)=a{x}^2+bx+c=0$ has at least one root in $(0,1)$