# Newton's Method¶

Copyright (C) 2020 Andreas Kloeckner

## MIT License

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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))
```

Out[86]:

[<matplotlib.lines.Line2D at 0x7f981263d630>]

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)
```

-1.324717957244746