The number of points where $f(x) = |\sin x|$ is not differentiable in $[0, 2\pi]$ is:
Step-by-Step Solution
Key Concept: $|\sin x|$ has corners wherever $\sin x = 0$ in $(0, 2\pi)$: at $x = \pi$ (and at $x = 0, 2\pi$ which are endpoints). In the open interval $(0, 2\pi)$, the only non-differentiable interior point is $x = \pi$. So the answer is 1... but if endpoints count: $x = 0, \pi, 2\pi$, giving 3 if we count boundary. For open interior: 1. At $x = \pi$: left derivative $= \cos \pi = -1$, right $= -\cos \pi = 1$. Not differentiable.
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Correct Answer: (2)