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4-163.

Use your expression for Newton's Method to find the root between [0, 1] of f(x) = 16x3 − 24x2 + 12x − 1 accurate to three decimal places. Homework Help ✎

First find the real root by solving: 0 = f(x)

Next find f '(x).

Start employing Newton's method. Stop when the approximate root and the real root agree to three decimal places.

Check your work as you go:
x1 = 0.2
x2 ≈ 0.0685
x3 ≈ 0.100
x4
x5
Remember to stop when the approximate root and the real root agree to three decimal places.