Question

$f\left(x\right)=\left[sinx\right],0<x<2\pi$ is not differentiable at:

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{2},\pi$
• C. $\pi$
• D. $\frac{\pi }{3},\pi$

Answer 1

The correct option is B $\frac{\pi }{2},\pi$



$f\left(x\right)=\left[sinx\right],0<x<2\pi .$
$\left[sinx\right]$.
From the graph of [sin x], we see that f(x) is not differentiable at x = $\frac{\pi }{2}$ and $\pi$ as
$f\left(x\right)=\left[sinx\right]=\{\begin{array}{cc}0:& 0<x<\frac{\pi }{2}\\ 1:& x=\frac{\pi }{2}\\ 0:& \frac{\pi }{2}<x\le \pi \\ -1:& \pi <x<2\pi \end{array}$
$\therefore$ f(x) is not differentiable at $x=\frac{\pi }{2},\pi$.