# Newton's Method

• Mar 26th 2010, 11:57 AM
creativename
Newton's Method
This is my first post, so I'm hoping that this is in the correct section
Use Newton's Method to find the two solutions

e^x=5.5x

https://webwork.math.lsu.edu/webwork...rob4image1.png

solve for
xleft=________
xright=_______
• Mar 26th 2010, 01:35 PM
TheEmptySet
Quote:

Originally Posted by creativename
This is my first post, so I'm hoping that this is in the correct section
Use Newton's Method to find the two solutions

e^x=5.5x

https://webwork.math.lsu.edu/webwork...rob4image1.png

solve for
xleft=________
xright=_______

Newton's method - Wikipedia, the free encyclopedia

Using this formula with $\displaystyle f(x)=e^{x}-5.5x \implies f'(x)=e^{x}-5.5$

$\displaystyle x_{n+1}=x_n-\frac{e^{x_n}-5.5x_n}{e^{x_n}-5.5}$

Note that $\displaystyle f(0)$ is positive and $\displaystyle f(1)$ is negative so taking a guess set $\displaystyle x_0=0.5$

Then just iterate the series until you get the desired accuracry

Here is a excel worksheet it only take 2 interations to get 4 decimal places of accuracy.
• Mar 27th 2010, 12:18 PM
creativename
thanks, using that method i was able to attain the left end point at
xleft=0.22846094

however I'm still uncertain of the right end point
thanks again for the quick reply!