### Use Newton's Method

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8 months ago by

Use Newton's method to determine xfor given function and given x0

$f\left(x\right)=x^3-7x^2+8x-3$ƒ (x)=x37x2+8x3

with X0 = 5

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8 months ago by

It is straight forward to solve. The basic formula for Newton's method is

Xn+1 = Xn -f(Xn)/f'(Xn)

so all we need to do is run through this twice.

Here is the derivative of the function since we’ll need that.

$f'\left(x\right)=3x^2-14x+8$ƒ '(x)=3x214x+8

For the first iteration

$X1=X0-\frac{f\left(X0\right)}{f'\left(X0\right)}=5-\frac{f\left(5\right)}{f'\left(5\right)}=5-\frac{-13}{13}=6$X1=X0ƒ (X0)ƒ '(X0) =5ƒ (5)ƒ '(5) =51313 =6

The second iternation

$X2=X1-\frac{f\left(X1\right)}{f'\left(X1\right)}=6-\frac{f\left(6\right)}{f'\left(6\right)}=6-\frac{9}{32}=5.71875$X2=X1ƒ (X1)ƒ '(X1) =6ƒ (6)ƒ '(6) =6932 =5.71875

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