Using Newton's method with the initial point

Using the TI-85 graphing calculator:

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- 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