Question

Let $f\left(x\right)=[17+4\sin x],x\in [\pi ,2\pi ]$. Then which of the following statement is/are correct ?

$([.]$ denotes the greatest integer function $)$

• A. $f\left(x\right)$ is differentiable at $x=\frac{3\pi }{2}$.
• B. $f\left(x\right)$ is non-differentiable exactly at $8$ points.
• C. $f\left(x\right)$ is non-differentiable exactly at $6$ points.
• D. $f\left(x\right)$ is non-differentiable exactly at $7$ points

Answer 1

Answer: (A), (C)

The correct options are
A $f\left(x\right)$ is differentiable at $x=\frac{3\pi }{2}$.
C $f\left(x\right)$ is non-differentiable exactly at $6$ points.

$f\left(x\right)=17+\left[4\sin x\right]$,
Now checking continuity and differentiability of $\left[4\sin x\right]$ by graph,


From graph it is clear that $f\left(x\right)$ is non-differentiable at $6$ points.

$f\left(x\right)$ is differentiable at $x=\frac{3\pi }{2}$