diff --git a/src/optimierung/newton_verfahren.py b/src/optimierung/newton_verfahren.py
index c34ef13..8c3ceff 100644
--- a/src/optimierung/newton_verfahren.py
+++ b/src/optimierung/newton_verfahren.py
@@ -1,16 +1,16 @@
-#%%
+# %%
 import numpy as np
 import sympy as sp
 import matplotlib.pyplot as plt
 
-#%%
+# %%
 # "Einfacher" Newton Verfahren
-# Parameter 
+# Parameter
 N = 200
-x = sp.Symbol('x')
+x = sp.Symbol("x")
 
 # Funktion
-f_sym = sp.sin(3*x)+0.02*x**2
+f_sym = sp.sin(3 * x) + 0.02 * x**2
 
 # Ableitungen
 f = sp.lambdify(x, f_sym, "numpy")
@@ -18,7 +18,7 @@ f_prime = sp.lambdify(x, sp.diff(f_sym, x), "numpy")
 f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy")
 
 # Daten
-x_data = np.linspace(0,10,N)
+x_data = np.linspace(0, 10, N)
 f_data = f(x_data)
 
 # Plot
@@ -34,14 +34,14 @@ plt.axis("image")
 startwerte = [6.6, 3.4, 8.38]
 
 # Iterationsformel
-x_n = lambda x: x - f_prime(x)/f_second(x)
+x_n = lambda x: x - f_prime(x) / f_second(x)
 
 # Iteration
 for x_0 in startwerte:
     n = 0
     x_i = x_0
     f_x_prime = f_prime(x_0)
-    print(f"n: {n}\nf(x): {x_0}\nf'(x): {f_x_prime}\n")
+    print(f"x_{n}: {x_0}\nf'(x_{n}): {f_x_prime}\n")
 
     limit = 4
 
@@ -49,17 +49,17 @@ for x_0 in startwerte:
         n += 1
         x_i = x_n(x_i)
         f_x_prime = f_prime(x_i)
-        print(f"n: {n}\nf(x): {x_i}\nf'(x): {f_x_prime}\n")
+        print(f"x_{n}: {x_i}\nf'(x_{n}): {f_x_prime}\n")
         limit -= 1
 
-#%%
+# %%
 # "Modifizierter" Newton Verfahren
-# Parameter 
+# Parameter
 N = 200
-x = sp.Symbol('x')
+x = sp.Symbol("x")
 
 # Funktion
-f_sym = sp.sin(3*x)+0.02*x**2
+f_sym = sp.sin(3 * x) + 0.02 * x**2
 
 # Ableitungen
 f = sp.lambdify(x, f_sym, "numpy")
@@ -67,7 +67,7 @@ f_prime = sp.lambdify(x, sp.diff(f_sym, x), "numpy")
 f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy")
 
 # Daten
-x_data = np.linspace(0,10,N)
+x_data = np.linspace(0, 10, N)
 f_data = f(x_data)
 
 # Plot
@@ -83,14 +83,14 @@ plt.axis("image")
 startwerte = [6.6, 3.4, 8.38]
 
 # Iterationsformel
-x_n = lambda x: x - f_prime(x)/np.abs(f_second(x))
+x_n = lambda x: x - f_prime(x) / np.abs(f_second(x))
 
 # Iteration
 for x_0 in startwerte:
     n = 0
     x_i = x_0
     f_x_prime = f_prime(x_0)
-    print(f"n: {n}\nf(x): {x_0}\nf'(x): {f_x_prime}\n")
+    print(f"x_{n}: {x_0}\nf'(x_{n}): {f_x_prime}\n")
 
     limit = 4
 
@@ -98,5 +98,6 @@ for x_0 in startwerte:
         n += 1
         x_i = x_n(x_i)
         f_x_prime = f_prime(x_i)
-        print(f"n: {n}\nf(x): {x_i}\nf'(x): {f_x_prime}\n")
-        limit -= 1
\ No newline at end of file
+        print(f"x_{n}: {x_i}\nf'(x_{n}): {f_x_prime}\n")
+        limit -= 1
+# %%