"The graph below is the graph of f', the derivative of f; The domain of the derivative -5≤x≤6"

1) The critical points for f are x=

2) The critical points for f' are x= -3, -2/3, 2, 4, 5.

3) F has a local maximum when x=

4) F has its maximum value on [-5,6] when x=

...

Is this information obtainable without knowing the original function or graphing the original function?

I would assume it is, but I'm not sure how to go about it?