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Differentiation question

2023 · 1 Feb · Shift 1 · Q30

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PYQ Library
JEE Main
Mathematics
Differentiation
2023 · 1 Feb · Shift 1 · Q30

Differentiation question

2023 · 1 Feb · Shift 1 · Q30

JEE MainMathematicsDifferentiationMCQ+4 / −1

Let

f(x) = 2x + {\tan ^{ - 1}}x

and

g(x) = {\log _e}(\sqrt {1 + {x^2}} + x),x \in [0,3]

. Then

A
there exists $\widehat x \in [0,3]$ such that $f'(\widehat x) \lt g'(\widehat x)$
B
there exist $0 \lt {x_1} \lt {x_2} \lt 3$ such that $f(x) \lt g(x),\forall x \in ({x_1},{x_2})$
C
$\min f'(x) = 1 + \max g'(x)$
D
$\max f(x) \gt \max g(x)$

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