Continuity and Differentiability_JEE-Main-2021_270721_S2 - Competishun

JEE MAIN 2021 S2

27-07-2021 S2

Question

Let $f:[0, \infty) \rightarrow[0,3]$ be a function defined by $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\max \{\sin \mathrm{t}: 0 \leq \mathrm{t} \leq \mathrm{x}\}, & 0 \leq \mathrm{x} \leq \pi \\ 2+\cos \mathrm{x}, & \mathrm{x}>\pi\end{array}\right.$ Then which of the following is true ?

Select the correct option:

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

ƒ is differentiable everywhere in $(0, \infty)$

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

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution