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

MCQ

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

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

✓

Answer

Correct option: B.

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

$\text{f(x)}=|\cos\text{x}|$
Given function is trigonometric function.
$\Rightarrow$ Hence, it is continuous.
Function is not differentiable at odd multiples of $\frac{\pi}{2}$
$\Rightarrow f(x)$ is not differentiable at $\text{x}=(2+\text{n}+1)\frac{\pi}{2}.$

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