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Another option is to use splines to approximate the curve. Here is some code inspired by

var('t y z')
Q=[ [float(t1),float(z1)] for t1,y1,z1 in P]
x_points=([p[0] for p in Q])
y_points=([p[1] for p in Q])
tmp = interpolate.splrep(x_points, y_points)
f=lambda x: interpolate.splev(x, tmp)

You could then find a zero using:


Also, you can compute the derivative using:

g=lambda x: interpolate.splev(x, tmp,der=1)

Then, find potential extrema using find_root.