How can I find all extreme points of the function (minimun and maximum)

Question

I want wo find out all extreme points of a function.

This is what I have tried so far:

import matplotlib.pyplot as plt
from scipy.signal import find_peaks

scale_factor = 0.01 
peaks, _ = find_peaks(derivation)
plt.plot(x_values[:-2], derivation)
plt.plot(peaks*scale_factor, derivation[peaks], "x")
plt.show()

This is the output:

The problem is that I would like to have all extreme points and not just the maxima. Could someone explain me how I can reach this? Because next I intend to compare the extreme points with each other. Thus I need the y-values too. But peaks gives me only the x-locations. Could anyone help me please? Thanks a lot.

This is my data:

derivation=[   9.88,   -2.12,   29.88,   -2.12,    9.88,   16.88,    9.88,
          4.88,    9.88,   -2.12,    9.88,   16.88,   10.88,    9.88,
         10.88,    9.88,    4.88,    3.88,   -2.12,    9.88,    3.88,
         10.88,   10.88,    9.88,    9.88,   10.88,   10.88,   15.88,
         16.88,   16.88,   22.88,   34.88,   41.88,   53.88,   60.88,
         -2.12,   72.88,   84.88,   97.88,  110.88,  128.88,  141.88,
        159.88,  172.88,  191.88,  203.88,  222.88,  241.88,  266.88,
        272.88,  297.88,  303.88,  322.88,  303.88,  279.88,  240.88,
        166.88,   97.88,   22.88,  -46.12,  -64.12,  -90.12, -139.12,
       -134.12, -164.12, -190.12,   -2.12, -202.12, -226.12, -221.12,
       -227.12, -234.12, -214.12, -214.12, -215.12, -215.12, -208.12,
       -196.12, -189.12, -183.12, -184.12, -189.12, -183.12, -177.12,
       -165.12, -152.12, -146.12,   -2.12, -152.12, -170.12, -171.12,
       -177.12, -171.12, -177.12, -170.12, -159.12, -133.12, -108.12,
        -77.12,  -52.12,  -27.12,   -8.12,   21.88,   47.88,   -2.12,
         73.88,   84.88,   91.88,  109.88,  122.88,  103.88,  110.88,
        110.88,  109.88,  109.88,  110.88,   91.88,   78.88,   66.88,
         53.88,   47.88,   34.88,   29.88,   -2.12,   22.88,   22.88,
         15.88,   16.88,   10.88,    3.88,    9.88,    4.88,   -2.12,
         16.88,   -2.12,    3.88,  -15.12,   -8.12,  -15.12,   -8.12,
         -8.12,   -2.12,   -8.12,   -8.12,   -9.12,   -8.12,   -8.12,
         -2.12,   -9.12]

and

x_values=[0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,
       0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,
       0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,
       0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,
       0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,
       0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,
       0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,
       0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,
       0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,
       0.99, 1.  , 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09,
       1.1 , 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, 1.19, 1.2 ,
       1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, 1.29, 1.3 , 1.31,
       1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 1.39, 1.4 , 1.41, 1.42,
       1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 1.5]
 

Answer 1

Sorry if I misunderstood what you meant in the comments; you can use scipy.signal.argrelextrema to compute both maxima and minima:

import matplotlib.pyplot as plt
import numpy as np
from scipy.signal import find_peaks, argrelextrema

derivation = np.array(derivation)
x_values = np.array(x_values)

scale_factor = 0.01
maxima = argrelextrema(derivation, np.greater)
minima = argrelextrema(derivation, np.less)
extrema = np.concatenate([maxima, minima], axis=None)
plt.plot(x_values[:-2], derivation)
plt.plot(extrema*scale_factor, derivation[extrema], "x")
plt.show()

And you can always use derivation[extrema], or derivation[peaks] in your original, to get the y-values associated with each peak.