How to calculate slopes at the inflection points?

[#1]

Hi, I would like to calculate the rates of product formation. For each sample, 180 time points were measured and fitted with Spline 0.75. I have already created the first derivatives. But I don't know how to get the slopes at the first inflection point. The slope at the second inflection point is less important, but it would be nice to have it too.

X: time (min)

Y: concentration (mg/mL)

Sort by Sample name

Thanks for your help

[#2 · Accepted solution]

from https://www.mathsisfun.com/calculus/inflection-points.html I re-learned:

"The second derivative tells us if the slope increases or decreases.

• When the second derivative is positive, the function is concave upward.
• When the second derivative is negative, the function is concave downward."

So the 2nd derivative is zero at the inflection point. The first derivative is the slope at that point.

[#3]

Hi Craige, Can you extract the slope at the inflection point from an analyze tool using JMP?

I'm trying to get that slope using the Fit Curve < Sigmoid Curves > Logistics Curves> Fit Logistic 3P

The curve looks great but now I don't know how to get the slope information. I can do it by excel but would prefer JMP to consequently use the same methodology.

Thank you for your feedback.

Wim

 

[#4]

You can right-click on the Parameter Estimates table and select Make Into Data Table.

You can also grab any of this information with a short script.

[#5]

Mark is suggesting the report contains the parameters for the function that draws the green line. You might be able to differentiate that function to determine the slope at the inflection point, and you can certainly use that function to calculate two values of Y just slightly to the left and right of the inflection point, then get the slope between those points (y1-y0)/(x1-x0).

Right-click the graph -> Customize to see the dialog with the formula for the green line.

[#6]

Or just get the formula here

I should have peeked here first!