Answer
$f$ is not differentiable at $x=2$ and $x=-1$.
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 2 points at which $f$ is not differentiable there:
- At $x=2$, the graph has a corner. So there cannot be any tangent line there, $f$ is not differentiable.
- At $x=-1$, the graph is not continuous. Therefore, $f$ is not differentiable there.
