Question

Use newton's method to approximate the solution to x^5-2=3x+1; find the third iteration using x1=1 as the initial guess.

Answer 1

\[x_2=x_1-\frac{f\left(x_1\right)}{f'\left(x_1\right)}\]

Answer 2

Rewrite function as

Answer 3

\[x^5-3x-3=0\]

Answer 4

\[1-\frac{\left(x^5-3x-3\right)}{5x^4-3}\]

Answer 5

Continueplz

Answer 6

Lets' plug in 1
\[1-\frac{\left(1^5-3(1)-3\right)}{5(1)^4-3}\]
=7/2

Answer 7

Now we have to do whole thing again with 7/2 instead of 1

Answer 8

So is 2.8 my final ans?

Answer 9

I got 2.28