Let f:[0, \infty) \\to[0,3] be a function defined by f(x)= \\begin{array}{c}\max \{\sin t: 0 \\leq t \\leq x\\end{array}{,}, 0 \\leq x \\leq \\pi; 2+\cos x{,} , x>\\piThen which of the following is true? [27 Jul 2021 Shift 2]

Correct Answer is : f is differentiable everywhere in (0,∞)

f is continuous everywhere but not differentiable exactly at one point in (0, \infty)

f is differentiable everywhere in (0, \infty)

f is not continuous exactly at two points in (0, \infty)

f is continuous everywhere but not differentiableexactly at two points in (0, \infty)

JEE Main 27 July 2021 Shift 2 Solved Paper

Section: Mathematics

Question : 74 of 90

Marks: +1, -0

Let f:[0,∞)→[0,3] be a function defined by

f(x)={

max{sin‌t:0≤t≤x}‌,	0≤x≤π
2+cos‌x‌,	x>π

Then which of the following is true?

[27 Jul 2021 Shift 2]

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