The function $f(x)=|\cos x|$ is

• A

  Everywhere continuous and differentiable
• Correct answer
  B

  Everywhere continuous but not differentiable at odd multiples of $\pi / 2$
• C

  Neither continuous nor differentiable at $(2 n+1) \frac{\pi}{2}, n \in Z$
• D

  Not differentiable everywhere

Solution

$f(x)=|\cos x|$ Graph of $f(x)=|\cos x|$
From graph we can see that $f(x)$ is not differentiable at points $\frac{\pi}{2}, \frac{3 \pi}{2}, \frac{-\pi}{2} \ldots$. . Also, it is everywhere continuous. i.e. At $x=(2 n+1) \frac{\pi}{2}, n \in Z$ $f(x)$ is not differentiable but, continuous everywhere.

Hence, the correct answer is option: 'B'.