The function \(f(x)=x^{3}-6 x^{2}+a x+b\) is such that \(f(2)=f(4)=0\). Consider two statements. \((S_1)\) there exists \(\mathrm{x}_{1}, \mathrm{x}_{2} \in(2,4), \mathrm{x}_{1}<\mathrm{x}_{2}\), such that \(f^{\prime}\left(x_{1}\right)=-1\) and \(f^{\prime}\left(x_{2}\right)=0\) \((S_2)\) there exists \(\mathrm{x}_{3}, \mathrm{x}_{4} \in(2,4), \mathrm{x}_{3}<\mathrm{x}_{4}\), such that \(f\) is decreasing in \(\left(2, x_{4}\right)\), increasing in \(\left(x_{4}, 4\right)\) and \(2 f^{\prime}\left(x_{3}\right)=\sqrt{3} f\left(x_{4}\right)\). Then

1. A both \((S_1)\) and \((S_2)\) are true
2. B \((S_1)\) is false and \((S_2)\) is true
3. C both \((S_1)\) and \((S_2)\) are false
4. D \((S_1)\) is true and \((S_2)\) is false