Let f ( x ) = | sin x | . Then

Question

Let $f (x) =$ $| \sin x |$ . Then

Smart Achievers · Accepted Answer

(2)

Ans. $f$ is everywhere continuous but not differentiable at $x = n π, n \in Z$

Explanation:

We have, $f (x) =$ $| \sin x |$

We know that $| x |$ and $\sin x$ are continuous for all real $x$ .

So, $| \sin x |$ is also continuous for all real $x$ .

Since, $| x |$ is non-differentiable at $x = 0$

therefore, $| \sin x |$ is non-differentiable when $\sin x = 0$ or $x = n π, n \in Z$

Hence, $f (x)$ is continuous everywhere but not differentiable at $x = n π, n \in Z .$

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