QJEEM21Mab74e: JEE Main 2021 Mathematics - Class 12 JEEM21Mab74e Solution: Let be a function defined by f ( x ) = { max { sin ⁡ t : 0 ≤ t…

Question

Verified Solution • 2025–26 Session moderate

Let

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

be a function defined by

f (x) = {\begin{matrix} max {\sin t : 0 \leq t \leq x}, & 0 \leq x \leq π \\ 2 + \cos x, & x > π \end{matrix}

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, $\infty$ )