import matplotlib.pyplot as plt
import numpy as np

# %% Function for funksjonen f():
def f(x):
    return x**3 - 6*x**2 + 9*x
    
# %% Funksjon for senterdifferanse:

def d2fdx2(f_vec, h):
    dobbelderiverte = np.zeros(len(f_vec)) + np.nan
    for i in range(1, len(f_vec)-1, 1):
        dobbelderiverte[i] = (f_vec[i+1] - 2*f_vec[i]
                        + f_vec[i-1])/h**2
    return dobbelderiverte 

dx = 0.01
x_start = 0.0
x_stop = 5.0
N = int ((x_stop - x_start)/dx + 1)
x_koor = np.linspace(x_start, x_stop, N)

f_func = f(x_koor)  # Funksjonsverdier
f_dderivert = d2fdx2(f_func, dx)  # Dobbelderivert

plt.close('all')
plt.figure(1, figsize=(12, 9))
plt.plot(x_koor, f_dderivert, label='d2f_dx2')
plt.legend()
plt.grid()
plt.xlabel('x')

# plt.savefig('plot_der_int_dobbelderiv.pdf')
plt.show()