Let f(x)=| |. then, - Vidyadip

MCQ

Let $\text{f(x)}=|\sin\text{x}|.$ then,

A
$f(x)$ is everywhere differentiable.
✓
$f(x)$ is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
C
$f(x)$ is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
D
None of these.

✓

Answer

Correct option: B.

$f(x)$ is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$

$\text{f(x)}=|\sin\text{x}|$
Given function is continuous and differentiable on $(2\text{n}\pi,(2\text{n}+1)\pi)$
But not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}.$
As $\sin\text{n}\pi=0$ for $\text{n}\in\text{Z}.$

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