Well, a point of inflection is where the concavity changes, so for that first link you posted the points of inflection would be found at A, C, E, and G.
Local maxima are the maximum points which are B and F.
f'(x) is increasing at point E. You would find this by graphing the derivative of the function and seeing where the slope increases.
I couldn't get the right answers for the question where f(x) decrease
But the rest after that, are pretty easy.
Hopefully this helped; ask if you need more help!