The function f(x)=| | is: 1. Differentiable atx=(2n+1) 2 ,n 2. Co… - Vidyadip

Question

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

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

✓

Answer

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

Solution:

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

Given function is trigonometric function.

⇒ Hence, it is continuous.

Function is not differentiable at odd multiples of $\frac{\pi}{2}$

⇒ f(x) is not differentiable at $\text{x}=(2+\text{n}+1)\frac{\pi}{2}.$

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