# Data Points where I need to identify where a tangent to the graph is vertical

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Mikkel Ibsen on 15 Feb 2017
Edited: Mikkel Ibsen on 16 Feb 2017
Hey Experts I need help to identify where a tangent is vertical on a data set that is represented by a graph.
Data_X = [.1 .2 .45 .79 1.29 1.35 1.4 1.925 2.45 2.95 3.36 3.82 3.99 4.16 4.32 4.415 4.51 5.4 5.46 5.575 5.69 5.68 5.73 5.78 5.83 5.93 6.8 6.11 6.15 6.19 6.21 6.24 6.25 6.26 6.14 6.5 6.6 6.7 6.5 6.35 6.2 6.7 6.15 6.14 6.1 5.99 5.85 5.7 5.58 5.61 5.71 5.72 5.57 5.25 4.97 4.64 4.45 4.37 4.31 4.28 4.32 4.39 4.42 4.45];
Data_Y = 1:length(Data_X);
I need to identify the data point where the tangent to the graph is vertical. I cannot make a function for this, because its only a small part of the graph. But if I can find it here, I can find it everywhere.
It cannot be found by maximum, since this is a small piece and there is a bigger value farther down, and Im interested in all of the vertical tangents.
Is there a person that can help me?
Best Retard Mikkel Roger Stafford on 15 Feb 2017
Your request is not clear to me. To make a graph of your data, it must be plotted against another variable. If that other variable is simply the index of the ‘data’ elements, it would be impossible to have a vertical tangent. If the other variable is not this, what is it?

Star Strider on 15 Feb 2017
I do not see that ‘Data’ has a ‘vertical’ slope anywhere. Perhaps supplying an independent data vector (since ‘Data’ is the dependent variable) and defining ‘vertical’ would help. The derivative provided by the gradient function would define the slope of ‘Data’ at any point, and nowhere is it high, much less approaching infinity (the definition I would use to define ‘vertical’).
figure(1)
plot(Data)
hold on
plot(dData)
hold off
grid
Mikkel Ibsen on 15 Feb 2017
Does this help? Data_X is the numbers as before, and Data_Y is just 1 to the number of inputs in Data_X, if you plot that it should be vertical, and there should be a point where the graph goes from negative slope to positive slope, I need to find the point where it changes, or a approximate area where it changes. Does that help you or do I need to make it more precise?
I know there isn't a point where the tangent is vertical, but in-between there is.