### Home > CALC > Chapter 4 > Lesson 4.5.1 > Problem4-163

4-163.

Use your expression for Newton's Method to find the root between $[0, 1]$ of $f(x) = 16x^3-24x^2 + 12x-1$ accurate to three decimal places.

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

Next find $f^\prime(x)$.

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.