How different “inflection point” is from “turning point” and “diverging point”?

Solution 1:

In this example, the inflection point marks exactly where things changed from good to bad, from boom to bust.

Turning point is where things changed, not necessarily from good to bad. Just changed direction, not related to quality.

Diverging point suggests where the disagreement starts. We had the same opinion once, and started to have different thoughts at that precise point.

Solution 2:

The sense in which the mathematical term inflection point can be applied to something like economics is the point at which things change from getting better to getting worse or the other way around. This is not the same as going from good to bad (or bad to good). This is about the rate of change of movement going from positive to negative or vice versa.

A turning point could be an inflection point, but it could also refer to a sudden change. Inflection points are generally gradual. Also, there is nothing about a turning point that implies that things will be going in the opposite direction, whereas inflection points do have that kind of implication.

Diverging and junctions have to to with separating and rejoining two paths, whereas both inflection points and turning points refer to single paths.