The function f(x)=| | is : - Vidyadip

MCQ

The function $\text{f(x)}=|\cos\text{x}|$ is :

A
Everywhere continuous and differentiable.
✓
Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
C
Neither continuous nor differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
D
None of these.

✓

Answer

Correct option: B.

Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$

As $\cos x$ is even function it is continuous everywhere but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
$\cos\Big[(2\text{n}+1)\frac{\pi}{2}=\cos\Big(\text{n}\pi+\frac{\pi}{2}\Big)\Big]=-\sin\text{n}\ \pi$
For $n$ as an integer
$\Rightarrow\sin\text{n}\ \pi=0$
For $n$ as rational
$\Rightarrow\sin\text{n}\ \pi=-1$

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