How do you find the first three iterate of the function f(x)=4x−3 for the given initial value x_0=2?

kakvoglq 2022-09-21 Answered
How do you find the first three iterate of the function f ( x ) = 4 x - 3 for the given initial value x 0 = 2 ?
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Answers (1)

Malcolm Flores
Answered 2022-09-22 Author has 8 answers
The Newton's method is x n + 1 = x n - f ( x n ) f ( x n )
Here f ( x ) = 4 x - 3 and f ( x ) = 4
And x 0 = 2
x 1 = x 0 - f ( x 0 ) f ( x 0 ) = 2 - 5 4 = 3 4

x 2 = x 1 - f ( x 1 ) f ( x 1 ) = 3 4 - 0 = 3 4

x 3 = x 2 - f ( x 2 ) f ( x 2 ) = 3 4 - 0
We obtain the same valuebecause f(x) is a linear function and the intercept with the x-axis is ( 3 4 , 0 )
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