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

Solution

1. The function $f(x)$ is a sum of two absolute value functions.
2. Absolute value functions $|x-a|$ are non-differentiable at $x=a$.
3. Here, the points of non-differentiability are $x=1$ and $x=2$.
4. Since the sum of non-differentiable functions at these points remains non-differentiable, there are 2 points.
5. Hence the answer is (C).