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import numpy as np
import matplotlib.pyplot as plt

def f(x):
    return 3*np.cos(x)**2 # Define the main function f(x)


def centered(x,dx): #Central difference approximate (second order)
    return (f(x-h)-2*f(x)+f(x+h))/h**2

def fdiff(x):
    return 6*np.sin(x)**2- 6*np.cos(x)**2

N=100 #number of slices
x_initial=0
x_final=2*np.pi
h=(x_final-x_initial)/float(N)
x=np.linspace(x_initial,x_final,h)

print(h)

plt.plot(x, f(x),"black")
plt.plot(x, centered (x,h),"blue")
plt.plot(x ,fdiff(x),"red")
plt.show()