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Limits Continuity and Differentiability question

2021 · 27 Jul · Shift 2 · Q34

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 27 Jul · Shift 2 · Q34

Limits Continuity and Differentiability question

2021 · 27 Jul · Shift 2 · Q34

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f:[0,\infty ) \to [0,3]

be a function defined by

f(x) = \left\{ {\begin{matrix} {\max \{ \sin t:0 \le t \le x\} ,} & {0 \le x \le \pi } \\ {2 + \cos x,} & {x \gt \pi } \\ \end{matrix} } \right.

Then which of the following is true?

A
f is continuous everywhere but not differentiable exactly at one point in (0, $\infty$ )
B
f is differentiable everywhere in (0, $\infty$ )
C
f is not continuous exactly at two points in (0, $\infty$ )
D
f is continuous everywhere but not differentiable exactly at two points in (0, $\infty$ )

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