Problem:
Using Newton's method with the initial point
x = 2
, find the root of the equation
f(x) = x
3
+ 5 x - 4.
Visualization:
Using the TI-85 graphing calculator:
[Press here to see animation again!]
First, enter the equation of the function:
y1 = x^3 + 5 x - 4
and press the
ENTER
key.
Next, enter the equation of the derivative:
y2 = 3 x^2 + 5
and press the
ENTER
key. (You could enter
y2 = der1(y1, x, x)
in place of the derivative.)
Enter the formula used in Newton's Method:
Z = x - y1 ÷ y2
and press the
ENTER
key.
Enter the initial value for
x
:
2
STO
x : Z
and press the
ENTER
key. The value for
Z
is displayed.
Press
STO
x : Z
and press the
ENTER
key to obtain the second iteration.
Continue by pressing
2nd ENTER
followed by the
ENTER
key to get another iteration.
After several repetitions of the previous step, we obtain the following table of values:
n
x
n
0
0
1
1.17647058824
2
0.79288335372
3
0.725663700148
4
0.724076385282
5
0.724075551387
6
0.724075551386
7
0.724075551386
