Use Newton's method to approximate the indicated root of the equation correct to six decimal places
The root of x^4-2x^3+5x^2-5 = 0 in the interval [1,2]
The root of x^4-2x^3+5x^2-5 = 0 in the interval [1,2]
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Start with x_0 = 1.0
Find f'(x) = 4x^3 - 6x^2 + 10x
Keep calculating x_n+1 = x_(n) - f(x_n)/f'(x_n) until you get six places.
Not too hard with a calculator. Easier with a spreadsheet.
I get 1.11615324013531
Here's a graph.
Find f'(x) = 4x^3 - 6x^2 + 10x
Keep calculating x_n+1 = x_(n) - f(x_n)/f'(x_n) until you get six places.
Not too hard with a calculator. Easier with a spreadsheet.
I get 1.11615324013531
Here's a graph.