CPM Homework Help : CALC Problem 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.

Step 1:

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

Step 2:

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

Step 3:

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

Answers:

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.