### Home > APCALC > Chapter 4 > Lesson 4.5.1 > Problem4-173

4-173.

Use the equation for Newton’s Method in the Math Notes box in this lesson to approximate the root of $f\left(x\right) = 16x^{3} – 24x^{2} +12x – 1$ in the interval $[0, 1]$, accurate to three decimal places.

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

Next find $f '\left(x\right)$.

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.