I would like to know why the tangent method, so used in chemistry, works. Indeed, the teachers seem to take this method for granted but not a single one has been able to justify it to me. So I leave it to you, sincerely hoping that you will help me.
I know that the equivalence point is the inflection point of the graph, but I can't see why this geometric method works. So I want to know using analysis why this works. Like, if I take the second derivative of it, or something like that but I didn't get anything, I couldn't arrive at a result.
Here are the details of the tangent method:
Draw a tangent line on the upper half of the curve, and a tangent line parallel to the previous tangent line in the lower part of the curve.
Then take the half distance between the two tangents.
Then draw the third tangent parallel to both passing by the midpoint of the distance.
