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Let \(f:\left[0,\text{ }\infty \right)\text{ }\to \text{ }\left[0,\text{ }3\right]\) be a function defined by \(f(x)=\le…

Q1

Let \(f:\left[0,\text{ }\infty \right)\text{ }\to \text{ }\left[0,\text{ }3\right]\) be a function defined by

\(f(x)=\left\{\begin{array}{cc}
\max \{\sin t: 0 \leq t \leq x\}, & 0 \leq x \leq \pi \\
2+\cos x, & x>\pi
\end{array}\right.\)

Then which of the following is true?

[JEE Main 2021, 27 Jul (Shift 2)]

a

\(f\) is differentiable everywhere in \( (0, \infty) \)

b

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

c

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

d

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

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