Let $f(x)=|x-1|+|x-2|+|x-3|$. The number of points where $f(x)$ is not differentiable is:

Solution

1. The function is defined as $f(x)=|x-1|+|x-2|+|x-3|$.
2. An absolute value function $|x-a|$ is non-differentiable at the point $x=a$.
3. The individual terms $|x-1|$, $|x-2|$, and $|x-3|$ are non-differentiable at $x=1$, $x=2$, and $x=3$, respectively.
4. Since the sum of functions is non-differentiable where any of its components are non-differentiable, $f(x)$ is non-differentiable at these three points.
5. Hence the answer is (D).