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Limits Continuity and Differentiability question

2024 · 27 Jan · Shift 2 · Q33

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 27 Jan · Shift 2 · Q33

Limits Continuity and Differentiability question

2024 · 27 Jan · Shift 2 · Q33

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Consider the function

f:(0,2) \rightarrow \mathbf{R}

defined by

f(x)=\frac{x}{2}+\frac{2}{x}

and the function

g(x)

defined by

g(x)=\left\{\begin{array}{ll} \min \lfloor f(t)\}, & 0\lt \mathrm{t} \leq x \text { and } 0 \lt x \leq 1 \\ \frac{3}{2}+x, & 1 \lt x \lt 2 \end{array} .\right. \text { Then, }

A
$g$ is continuous but not differentiable at $x=1$
B
$g$ is continuous and differentiable for all $x \in(0,2)$
C
$g$ is not continuous for all $x \in(0,2)$
D
$g$ is neither continuous nor differentiable at $x=1$

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