Let f(x)=| |. Then, 1. f(x) is everywhere differentiable. 2. f(x)… - Vidyadip

Question

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

f(x) is everywhere differentiable.
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 $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
None of these.

✓

Answer

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

Solution:

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

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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