The function \(f(x)=x^3-6 x^2+a x+b\) is such that \(f(2)=f(4)=0\). Consider two statements.\(\l.... VIDEO
The function \(f(x)=x^3-6 x^2+a x+b\) is such that \(f(2)=f(4)=0\). Consider two statements.\(\left(S_1\right)\) : there exists \(x_1, x_2 \in(2,4), x_1<x_2\), such that \(f^{\prime}\left(x_1\right)=-1\) and \(f^{\prime}\left(x_2\right)=0\).\(\left(S_2\right)\) : 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 \(2 f^{\prime}\left(x_3\right)\) \(=\sqrt{3} f\left(x_4\right)\). š²PW App Link - https://bit.ly/YTAI_PWAP šPW Website - https://www.pw.live
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