### Home > CALC > Chapter 4 > Lesson 4.5.1 > Problem 4-163

4-163.

Use your expression for Newton's Method to find the root between [0, 1] of *f*(*x*) = 16*x*^{3} − 24*x*^{2} + 12*x *− 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: *x*_{1} = 0.2*x*_{2} ≈ 0.0685*x*_{3} ≈ 0.100*x*_{4} ≈*x*_{5} ≈

Remember to stop when the approximate root and the real root agree to three decimal places.