CPM Homework Help : APCALC Problem 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.

Step 1:

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

Step 2:

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

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.