Answer
$f$ is not differentiable at the points where $x=-4$, $x=-1$, $x=2$ and $x=5$.
Work Step by Step
There are 3 cases at which a function fails to be differentiable at a point:
1) Its graph has a corner or a kink there, since there is no tangent line at a corner or a kink.
2) The graph of the function is not continuous at that point. Not continuous means not differentiable.
3) The graph has a vertical tangent line at that point. Because a vertical tangent line would lead to $\lim\limits_{x\to a}|f'(x)|=\infty$
In this graph, there are 4 points at which function $f$ is not differentiable:
1) The point where $x=-4$, since the graph is not continuous there.
2) The point where $x=-1$, since the graph has a corner / a kink there.
3) The point where $x=2$, since the graph is again not continuous there.
4) The point where $x=5$, since at that point, only a vertical tangent line can be drawn.
