Identify concave up, down and points of inflexion by looking at a graph

Question

Provide the open intervals on which f is concave upwards, concave downwards, and provide the coordinates of each point of inflection.

I tried a few things. I understand that i should try to get the graph of f'(x) which I can do by looking at where the slope here is 0, then piecing together a rough image. But I failed to get the right answer.

Answer 1

Concave up: (- ∞, 2), (5, ∞)

Concave down: (2, 5)

Inflexion points: (2, 4); (5, 4)