Answer
The graph is not differentiable at $x=-2$, $x=1$ and $x=3$
Work Step by Step
There are 3 cases at which a graph is not differentiable at a point:
- There is a corner (a pointy shape) at a point in the graph (a pointy point cannot have any tangent lines there)
- The graph is not continuous at that point (differentiable means continuous)
- There is a vertical tangent line at that point in the graph (since $f'(x)=\infty$)
In this graph, there are 3 points at which $f$ is not differentiable there:
- At $x=-2$ and $x=3$, the graph has a kink/corner. That means there is no tangent line that can be drawn there. Therefore, $f$ is not differentiable there.
- At $x=1$, the graph is not continuous. Therefore, $f$ is not differentiable there.
