Let \(f(x)=2 x+\tan ^{-1} x\) and \(g(x)=\log _e\left(\sqrt{1+x^2}+x\right), x\) \(\in[0,3]\). Then [JEE Main 2023, 1 Fe…

There exists \(x \in[0,3]\) such that \(f^{\prime}(x)<g^{\prime}(x)\)

There exist \(0<x_1<x_2<3\) such that \(f(x)<g(x)\), \(\forall x \in\left(x_1, x_2\right)\)

\(\max f(x)>\max g(x)\)

\(\min f^{\prime}(x)=1+\max g^{\prime}(x)\)