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Provide solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Fill in the blanks question 6

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Hint: If $f(x)$ is differentiable at all $x\in R$ , we must show $f'(x)$ exists at all $x\in R$

Given: $f(x)=|\sin x|,\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

Solution:

We know that $f(x)=|\sin x|$ is continuous everywhere but not differentiable at integer multiples of $\pi$ and at $x=0$ .

At $x=0$ and $x=k\pi$ ( $k$ is an integer),

From the graph, $x = 0$ at this point $\left | \sin x \right |$ is not differentiable.

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