Let $f(x) = 2x + {\tan ^{ - 1}}x$ and $g(x) = {\log _e}(\sqrt {1 + {x^2}} + x),x \in [0,3]$. Then

Question

there exists $\widehat x \in [0,3]$ such that $f'(\widehat x) < g'(\widehat x)$

there exist $0 < {x_1} < {x_2} < 3$ such that $f(x) < g(x),\forall x \in ({x_1},{x_2})$

$\min f'(x) = 1 + \max g'(x)$

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

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