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Hi everyone,

I want to use a word instead of "where the slope of the curve changes" in a scientific text. Could you please help me? Thanks a lot. Here is my sentence:

The ???? points in the plot indicate changes in the flow properties of the porous medium.

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The slope of a curve is determined by taking the first derivative of the function. The rate of change of the slope is the second derivative.

In motion, the position is plotted as a function of time. The first derivative is called velocity or speed (rate of change per unit of time), and the second, acceleration (rate of change of velocity.)

https://www.mathsisfun.com/calculus/derivatives-introduction.html

You might be looking for "inflection point" - where the direction of the slope changes e.g. from positive to negative.

https://www.mathsisfun.com/calculus/inflection-points.html

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Vahid6105"where the slope of the curve changes"

On continuous curve, the slope can be changing continuously - over the entire domain. There are special points where it reverses direction: inflection points.

Are you trying to describe discontinuities where the second derivative is undefined?

https://www.dummies.com/education/math/calculus/how-to-know-when-a-derivative-doesnt-exist/

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Thanks AlpheccaStars. It was really helpful but no, I am not looking for inflection point. See the attached picture. I am looking for the point where the slope changes (arrow).

The photo is from:

https://www.mathsisfun.com/calculus/inflection-points.html

 AlpheccaStars's reply was promoted to an answer.
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Sorry. I didn't see the second part of your reply. You are right. The slope changes continuously. So, what is the name of this point? (attached photo)

There is no special name in mathematics that I know of for a general point of a curve as different from any other point.

"Critical points" are where the first derivative is 0. These are local minima, local maxima and inflection points. Every other point is just a point on the curve.

Is you problem in thermodynamics or mathematics?

Thanks again. Actually, I am working with porosity and permeability data of a porous medium (a rock). I plot the cumulative data against each other and any change in the slope (now I think a major change) indicates boundary of a zone with different reservoir properties. May be I just say any major change in the slope. What do you think?

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Vahid6105Actually, I am working with porosity and permeability data of a porous medium (a rock).

I think you are talking about the petrophysical response of a formation to a probe in wireline logging, or maybe analysis of cores. It is not an abstract mathematical curve, but measured data.

I recommend that you use the vocabulary of petrophysicists. They have a dedicated Wiki.

https://petrowiki.org/PEH:Acoustic_Logging

Vahid6105May be I just say any major change in the slope

Perhaps you should specify what "major" is....