Number of points of non-differentiablity in a graph

Question

Hahaha it seems all my questions are going to be calculus-based. :P

Another doubt, here's the question:

Let $f(x) = \max(\cos x,\hspace{2mm} x, \hspace{2mm}x-1)$, where $x \geq 0$. Then number of points of non-differentiablity of $f(x)$ is: $?$

By simply drawing a graph we can see that:

The graph of $f(x) = \max(\cos x,\hspace{2mm} x, \hspace{2mm}x-1)$, $x \geq 0$ follows the graph of $y = \cos(x)$ till approximately $x = 0.739$, after which it follows the graph of $y = x$.

This gives us 2 points of non differentiability:

1. One at $x=0$, which is an end-point of the graph.
2. One at $x = 0.739$, at which point the graph changes its branch creating a sharp corner.

I guess that's the only places the graph is non-differentiable. So my answer to the question would be $2$.

However! The answer in the answer script is $5$! As I've said in my previous question - my professor was confident that there are no errors in the paper, so I'm wondering whether there are actually $5$, or is it an error?

Answer 1

You are right there are 2 points of non differentiability.
1. Curve end point.
2. Defination change.