The function \(f(x)=x^3-6 x^2+a x+b\) is such that \(f(2)=f(4)=0\). Assertion (A): there exists \(x_1, x_2 \in(2,4), x_1…

The function \(f(x)=x^3-6 x^2+a x+b\) is such that \(f(2)=f(4)=0\).
Assertion (A): there exists \(x_1, x_2 \in(2,4), x_1<x_2\), such that \(f^{\prime}\left(x_1\right)=-1\) and \(f^{\prime}\left(x_2\right)=0\).
Reason (R): there exists \(x_3, x_4 \in(2,4), x_3<x_4\), such that \(f\) is decreasing in \(\left(2, x_4\right)\), increasing in \(\left(x_4, 4\right)\) and \(2 f^{\prime}\left(x_3\right)\) \(=\sqrt{3} f\left(x_4\right)\).

[JEE Main 2021, 1 Sep (Shift 2)]