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

MCQ

Let $\text{f(x)}=|\cos\text{x}|.$ Then,

A
$f(x)$ is everywhere differentiable.
B
$f(x)$ is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
✓
$f(x)$ 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: C.

$f(x)$ is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$

$\text{f}(\text{x)} = |\cos\text{x}|$
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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