# How to prove newton's method?

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As above. Thanks

As above. Thanks

##### 1 Answer

# x_(n+1) = x_n - f(x_n)/(f'(x_n)) #

#### Explanation:

Suppose we seek a solution to the equation:

# f(x) = 0 #

And that we have an initial estimate

The tangent to the curve at he point

# y - f(x_0) = f'(x_0)(x-x_0) #

The point

# 0 - f(x_0) = f'(x_0)(x_1-x_0) #

And if we rearrange for

# :. f'(x_0)(x_1-x_0) = -f(x_0) #

# :. x_1-x_0 = -f(x_0)/(f'(x_0)) #

# :. x_1 = x_0 - f(x_0)/(f'(x_0)) #

Leading to the general Newton's Method iterative method:

# x_(n+1) = x_n - f(x_n)/(f'(x_n)) #