# ## MIT License

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# of this software and associated documentation files (the "Software"), to deal
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# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
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#
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# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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#

# In[85]:
import numpy as np
import matplotlib.pyplot as pt
# Here's a function:
# In[86]:
def f(x):
return x**3 - x +1
def df(x):
return 3*x**2 - 1
xmesh = np.linspace(-2, 2, 100)
pt.ylim([-3, 10])
pt.plot(xmesh, f(xmesh))
# In[87]:
guesses = [2]
# Evaluate this cell many times in-place (using Ctrl-Enter)
# In[84]:
x = guesses[-1] # grab last guess
slope = df(x)
# plot approximate function
pt.plot(xmesh, f(xmesh))
pt.plot(xmesh, f(x) + slope*(xmesh-x))
pt.plot(x, f(x), "o")
pt.ylim([-3, 10])
pt.axhline(0, color="black")
# Compute approximate root
xnew = x - f(x) / slope
guesses.append(xnew)
print(xnew)