How to obtain the derivative of a function from this graph? Also, where $f'(x)$ is not defined?
I noticed that points $1$, $4$ and $0$ is where the graph has a corner (is this correct?). Any other points where it is not differentiable?
Also, about the derivative of the graph, any clue would be appreciated.
Your reasoning is right for the interior points and note that we also need to include the boundary points $x=-4$ and $x=6$ among those where $f'(x)$ is not defined, if these are included in the domain for $f(x)$.
For the graph of the derivative we exclude the corner and boudary points and evaluate f'(x) in between, which is a contant value for each interval, according to
$$f'(x)=\frac{y_2-y_1}{x_2-x_1}\quad x_1 <x<x_2 $$