jee-main 2023 Q73

jee-main · India · session1_01feb_shift1 Differentiating Transcendental Functions Monotonicity or convexity of transcendental functions

Let $f(x) = 2x + \tan^{-1} x$ and $g(x) = \log_e\left(\sqrt{1 + x^2} + x\right)$, $x \in [0, 3]$. Then
(1) There exists $x \in (0, 3)$ such that $f'(x) < g'(x)$
(2) $\max f(x) > \max g(x)$
(3) There exist $0 < x_1 < x_2 < 3$ such that $f(x) < g(x)$, $\forall x \in (x_1, x_2)$
(4) $\min f'(x) = 1 + \max g'(x)$

Let $f(x) = 2x + \tan^{-1} x$ and $g(x) = \log_e\left(\sqrt{1 + x^2} + x\right)$, $x \in [0, 3]$. Then\\
(1) There exists $x \in (0, 3)$ such that $f'(x) < g'(x)$\\
(2) $\max f(x) > \max g(x)$\\
(3) There exist $0 < x_1 < x_2 < 3$ such that $f(x) < g(x)$, $\forall x \in (x_1, x_2)$\\
(4) $\min f'(x) = 1 + \max g'(x)$

Paper Questions

Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76 Q77 Q78 Q79 Q80 Q81 Q82 Q83 Q84 Q85 Q86 Q87 Q88 Q89 Q90