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.