Mathematics · 2021
JEE Main · 27 July 2021, Shift 2 · Q65
Let f:[0, ∞) →[0,3] be a function defined by f(x)= {max { sin t: 0 ≤ t ≤ x}, 0 ≤ x ≤ π; 2+ cos x, x>π} Then which of the following is true?
Let $\displaystyle f:[0, \infty) \rightarrow[0,3]$ be a function defined by
$$f(x)= \begin{cases}\max \{\sin \mathrm{t}: 0 \leq \mathrm{t} \leq x\}, & 0 \leq x \leq \pi \\ 2+\cos x, & x>\pi\end{cases}
$$
Then which of the following is true ?
Official answer
(4)
$\displaystyle f$ is differentiable everywhere in $\displaystyle (0, \infty)$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.