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An inflection point is where progress starts to decelerate ahead of a possible reversal in direction.

An inflection point is where the curvature (second derivative) changes sign. For example, it is where a function changes from concave to convex. It can apply both ways.

An inflection point is the point where a function changes sign. This can be both a positive or a negative indication.

This article carries a positive tone, so what they probably mean is that ICS to Android is the point where people start saying more positive than negative stuff about Android.

I think it's actually where the second derivative (concavity) of a function changes sign; but you're right in that it can be a positive as much as a negative indication.

No it's where the second derivative changes sign. You can think of the first derivative as the motion, and the second derivative as the "force" that's driving the motion - the force is changing direction.

Equivalently it is where the second derivative is equal to zero -- which implies the first derivative is at a local extrema.

In the context here, it's clear that the inflection point would be the point of greatest change.

Well not quite equivalent exactly - the second derivative could just touch zero and then go back whence it came :) That wouldn't be an inflection point I think, I'm not sure what you'd call that...

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