$f$ is not differentiable at $x=0$ and $x=-4$
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 $x=-4$, the graph has a corner. So there is not tangent line there, $f$ is not differentiable. - At $x=0$, the graph is not continuous. Therefore, $f$ is not differentiable there.